Research

Books, or parts of books

[B1] "Continuous Geometry",

F. Wehrung, Appendix D in George Grätzer, General Lattice Theory. Second Edition, Birkhäuser Verlag, Basel. 1998. xix+663 pp, pages 531--538.

[B2] "Lattice Theory: Special Topics and Applications. Volume 1".

G. Grätzer and F. Wehrung, editors,

doi: 10.1007/978-3-319-06413-0 , Birkhäuser (2014), xiii+468 pages. With contributions from G. Czédli, G. Grätzer, K. Keimel, J.P.S. Kung, J. Lawson, A. Pultr, J. Sichler, F. Wehrung.

[B3] "Lattice Theory: Special Topics and Applications. Volume 2".

G. Grätzer and F. Wehrung, editors,

doi: 10.1007/978-3-319-44236-5 , Birkhäuser (2016), xv+616 pages. With contributions from K. Adaricheva, N. Caspard, R. Freese, G. Grätzer, P. Jipsen, J.B. Nation, N. Reading, H. Rose, F. Wehrung.

Journal papers and preprints

[1] Non absoluité d'injections élémentaires,

F. Wehrung, Comptes Rendus de l'Académie des Sciences Paris, Série I, t. 304, no. 17 (1987), 503--505.

[2] Nonabsoluteness of elementary embeddings,

F. Wehrung, Journal of Symbolic Logic 54, no. 3 (1989), 774--778.

[3] Théorème de Hahn-Banach et paradoxes continus ou discrets,

F. Wehrung, Comptes Rendus de l'Académie des Sciences Paris, Série I, t. 310 (1990), 303--306.

HAL ccsd-00004714

[4] The Hahn-Banach Theorem implies the existence of a non-Lebesgue measurable set,

M. Foreman and F. Wehrung, Fundamenta Mathematicae 138, no. 1 (1991), 13--19.

HAL ccsd-00004713

[5] Gerbes primitives,

F. Wehrung, Comptes Rendus de l'Académie des Sciences Paris, Série I, t. 313 (1991), 357--362.

HAL ccsd-00004806

[6] Injective positively ordered monoids I,

F. Wehrung, Journal of Pure and Applied Algebra 83, no. 1 (1992), 43--82.

HAL ccsd-00004711

[7] Injective positively ordered monoids II,

F. Wehrung, Journal of Pure and Applied Algebra 83, no. 1 (1992), 83--100.

HAL ccsd-00004712

[8] Metric properties of positively ordered monoids,

F. Wehrung, Forum Mathematicum 5, no. 5 (1993), 183--201.

HAL ccsd-00004710

[9] Boolean universes above Boolean models,

F. Wehrung, Journal of Symbolic Logic 58, no. 4 (1993), 1219--1250.

HAL ccsd-00004693

[10] Restricted injectivity, transfer property and decompositions of separative positively ordered monoids,

F. Wehrung, Communications in Algebra 22, no. 5 (1994), 1747--1781.

HAL ccsd-00004694

[11] Common extensions of semigroup-valued charges,

HAL ccsd-00004679

[12] Baire paradoxical decompositions need at least six pieces,

F. Wehrung, Proceedings of the American Mathematical Society 121, no. 2 (1994), 643--644.

HAL ccsd-00004680

[13] The universal theory of ordered equidecomposability types semigroups,

F. Wehrung, Canadian Journal of Mathematics 46, no. 5 (1994), 1093--1120.

HAL ccsd-00004671

[14] Treillis bi-locaux équationnellement compacts,

F. Wehrung, Comptes Rendus de l'Académie des Sciences Paris, Série I, t. 318 (1994), 5--9.

HAL ccsd-00004678

[15] Equational compactness of bi-frames and projection algebras,

F. Wehrung, Algebra Universalis 33, no. 4 (1995), 478--515.

HAL ccsd-00004209

[16] Bounded countable atomic compactness of ordered groups,

F. Wehrung, Fundamenta Mathematicae 148 (1995), 101--116.

HAL ccsd-00004657

[17] A compactness property of Dedekind σ-complete f-rings,

F. Wehrung, Algebra Universalis 36, no. 4 (1996), 511--522.

HAL ccsd-00004655

[18] Monoids of intervals of ordered abelian groups,

F. Wehrung, Journal of Algebra 182, no. 1 (1996), 287--328.

HAL ccsd-00004068

[19] Monotone σ-complete groups with unbounded refinement,

F. Wehrung, Fundamenta Mathematicae 151 (1996), 177--187.

HAL ccsd-00004375

[20] Tensor products of structures with interpolation,

F. Wehrung, Pacific Journal of Mathematics 176, no. 1 (1996), 267--285.

HAL ccsd-00004374

[21] Norm-closed intervals of norm-complete ordered abelian groups,

F. Wehrung, Positivity 1, no. 3 (1997), 271--290.

arXiv math.GM/0501460 and HAL ccsd-00004067

[22] Embedding simple commutative monoids into simple refinement monoids,

F. Wehrung, Semigroup Forum 56, no. 1 (1998), 104--129.

arXiv math.GM/0503155 and HAL ccsd-00004373

[23] Non-measurability properties of interpolation vector spaces,

F. Wehrung, Israel Journal of Mathematics 103, no. 1 (1998), 177--206.

HAL ccsd-00004065

[24] Congruence lattices of free lattices in non-distributive varieties,

M. Ploščica, J. Tůma, and F. Wehrung, Colloquium Mathematicum 76, no. 2 (1998), 269--278.

arXiv math.GM/0501459 and HAL ccsd-00004064

[25] A uniform refinement property for congruence lattices,

F. Wehrung, Proceedings of the American Mathematical Society 127, no. 2 (1999), 363--370.

arXiv math.GM/0501458 and HAL ccsd-00004063

[26] The dimension monoid of a lattice,

F. Wehrung, Algebra Universalis 40, no. 3 (1998), 247--411.

arXiv math.GM/0501437 and HAL ccsd-00004052

[27] The M₃[D] construction and n-modularity,

G. Grätzer and F. Wehrung, Algebra Universalis 41, no. 2 (1999), 87--114.

arXiv math.GM/0501430 and HAL ccsd-00004046

[28] Proper congruence-preserving extensions of lattices,

G. Grätzer and F. Wehrung, Acta Mathematica Hungarica 85, no. 1-2 (1999), 169--179.

arXiv math.GM/0501438 and HAL ccsd-00004053

[29] Flat semilattices,

G. Grätzer and F. Wehrung, Colloquium Mathematicum 79, no. 2 (1999), 185--191.

arXiv math.GM/0501431 and HAL ccsd-00004047

[30] Tensor products and transferability of semilattices,

G. Grätzer and F. Wehrung, Canadian Journal of Mathematics 51 (1999), 792--815.

arXiv math.GM/0501419 and HAL ccsd-00004045

[31] A new lattice construction: the box product,

G. Grätzer and F. Wehrung, Journal of Algebra 221, no. 1 (1999), 315--344.

arXiv math.GM/0501418 and HAL ccsd-00004044

[32] Finitely presented and coherent ordered modules and rings,

F. Wehrung, Communications in Algebra 27, no. 12 (1999), 5893--5919.

arXiv math.GM/0501433 and HAL ccsd-00004049

[33] Congruence amalgamation of lattices,

G. Grätzer, H. Lakser, and F. Wehrung, Acta Sci. Math. (Szeged) 66, no. 1-2 (2000), 339--358.

arXiv math.GM/0501370 and HAL ccsd-00004029

[34] Tensor products of semilattices with zero, revisited,

arXiv math.GM/0501436 and HAL ccsd-00004051

[35] Finitely presented, coherent and ultrasimplicial ordered abelian groups,

arXiv math.GM/0501432 and HAL ccsd-00004048

[36] The Strong Independence Theorem for automorphism groups and congruence lattices of arbitrary lattices,

G. Grätzer and F. Wehrung, Advances in Applied Mathematics 24, no. 3 (2000), 181--221.

HAL ccsd-00004030

[37] Representations of distributive semilattices in ideal lattices of various algebraic structures,

K. R. Goodearl and F. Wehrung, Algebra Universalis 45, no. 1 (2001), 71--102.

arXiv math.GM/0501435 and HAL ccsd-00004050

[38] A survey of tensor products and related constructions in two lectures,

G. Grätzer and F. Wehrung, Algebra Universalis 45 , no. 2/3 (2001), 117--134.

arXiv math.GM/0501416 and HAL ccsd-00004041

[39] Representation of algebraic distributive lattices with ℵ₁ compact elements as ideal lattices of regular rings,

arXiv math.GM/0501367 and HAL ccsd-00004026

[40] Simultaneous representations of semilattices by lattices with permutable congruences,

arXiv math.GM/0501417 and HAL ccsd-00004042

[41] Unsolvable one-dimensional lifting problems for congruence lattices of lattices,

J. Tůma and F. Wehrung, Forum Mathematicum 14, no. 4 (2002), 483--493.

arXiv math.GM/0501377 and HAL ccsd-00004023

[42] Join-semilattices with two-dimensional congruence amalgamation,

F. Wehrung, Colloquium Mathematicum 93, no. 2 (2002), 209--235.

arXiv math.GM/0501372 and HAL ccsd-00004022

[43] Solutions to five problems on tensor products of lattices and related matters,

F. Wehrung, Algebra Universalis 47, no. 4 (2002), 479--493.

arXiv math.GM/0501371 and HAL ccsd-00004024

[44] From join-irreducibles to dimension theory for lattices with chain conditions,

arXiv math.GM/0501404 and HAL ccsd-00004017

[45] On the number of join-irreducibles in a congruence representation of a finite distributive lattice,

arXiv math.GM/0501366 and HAL ccsd-00004027

[46] Forcing extensions of partial lattices,

F. Wehrung, Journal of Algebra 262, no. 1 (2003), 127--193.

arXiv math.GM/0501378 and HAL ccsd-00004025

[47] The complete dimension theory of partially ordered systems with equivalence and orthogonality,

K.R. Goodearl and F. Wehrung, Memoirs of the American Mathematical Society, Vol. 176, no. 831 (July 2005), viii+117~p.

download dvi file, pdf file. See also arXiv math.GM/0403057.

[48] Direct decompositions of non-algebraic complete lattices,

F. Wehrung, Discrete Mathematics, Volume 263, Issues 1-3 (28 February 2003), Pages 311--321.

arXiv math.GM/0501373 and HAL ccsd-00004019

[49] Liftings of diagrams of semilattices by diagrams of dimension groups,

J. Tůma and F. Wehrung, Proceedings of the London Mathematical Society 87, no. 3 (2003), 1--28.

arXiv math.GM/0501376 and HAL ccsd-00004021

[50] Embedding finite lattices into finite biatomic lattices,

K. Adaricheva and F. Wehrung, Order 20, no. 1 (2003), 31--48.

HAL ccsd-00004018

[51] A survey of recent results on congruence lattices of lattices,

J. Tůma and F. Wehrung, Algebra Universalis 48, no. 4 (2002), 439--471.

arXiv math.GM/0501375 and HAL ccsd-00004020

[52] Sublattices of lattices of order-convex sets, I. The main representation theorem,

M. Semenova and F. Wehrung, Journal of Algebra 277, no.~2 (2004), 825--860.

arXiv math.GM/0501341 and HAL ccsd-00003980

[53] Sublattices of lattices of order-convex sets, II. Posets of finite length,

arXiv math.GM/0501340 and HAL ccsd-00003979

[54] Sublattices of lattices of order-convex sets, III. The case of totally ordered sets,

arXiv math.GM/0501339 and HAL ccsd-00003977

[55] Lattices of convex subsets of vector spaces,

M. Semenova and F. Wehrung, Algebra i Logika 43, no. 3 (2004), 261--290, translated in Algebra and Logic 43, no. 3 (2004), 145--161.

download ps file (Russian version)

arXiv math.GM/0501324 and HAL ccsd-00003955

[56] Semilattices of finitely generated ideals of exchange rings with finite stable rank,

F. Wehrung, Transactions of the American Mathematical Society 356, no. 5 (2004), 1957--1970.

arXiv math.GM/0501326 and HAL ccsd-00003951

[57] Sublattices of complete lattices with continuity conditions,

F. Wehrung, Algebra Universalis 53, no 2-3 (2005), 149--173.

arXiv math.GM/0501325 and HAL ccsd-00003949

[58] Von Neumann coordinatization is not first-order,

F. Wehrung, Journal of Mathematical Logic 6, no. 1 (2006) 1--24.

arXiv math.GM/0409250 and HAL ccsd-00002843 (see comments on the HAL page)

[59] Distributive semilattices as retracts of ultraboolean ones; functorial inverses without adjunction,

F. Wehrung, Journal of Pure and Applied Algebra 202, no. 1--3 (November 2005), 201--229.

arXiv math.GM/0409263 and HAL ccsd-00002854

[60] Lifting retracted diagrams with respect to projectable functors,

F. Wehrung, Algebra Universalis 54, no. 3 (2005), 349--371.

arXiv math.GM/0409270 and HAL ccsd-00002855

[61] Semilattices of groups and inductive limits of Cuntz algebras,

K.R. Goodearl, E. Pardo, and F. Wehrung, Journal für die Reine und Angewandte Mathematik 588 (2005), 1--25.

arXiv math.OA/0408072 and HAL ccsd-00002856

[62] Congruence lifting of diagrams of finite Boolean semilattices requires large congruence varieties,

J. Tůma and F. Wehrung, International Journal of Algebra and Computation 16, no. 3 (2006), 541--550.

arXiv math.GM/0410576 and HAL ccsd-00003186

[63] Distributive congruence lattices of congruence-permutable algebras,

P. Růžička, J. Tůma, and F. Wehrung, Journal of Algebra 311, no. 1 (2007), 96--116.

arXiv math.GM/0505381 and HAL ccsd-00004922

[64] A K₀-avoiding dimension group with an order-unit of index two,

F. Wehrung, Journal of Algebra 301, no. 2 (15 July 2006), 728--747.

arXiv math.GM/0505426 and HAL ccsd-00004942

[65] Non-extendability of semilattice-valued measures on partially ordered sets,

F. Wehrung, Contributions to General Algebra 17, Proceedings of the Vienna Conference 2005 (AAA 70), Verlag Johannes Heyn, Klagenfurt 2006, 191--200.

arXiv math.GM/0510303 and HAL ccsd-00012068

[66] Semilattices of groups and nonstable K-theory of extended Cuntz limits,

E. Pardo and F. Wehrung, K-Theory 37, no. 1-2 (2006), 1--23.

arXiv math.OA/0511272 and HAL ccsd-00013765

[67] Poset representations of distributive semilattices,

F. Wehrung, International Journal of Algebra and Computation 18, no. 2 (March 2008), 321--356.

arXiv math.GM/0601058 and HAL ccsd-00016421

[68] A solution to Dilworth's Congruence Lattice Problem,

F. Wehrung, Advances in Mathematics 216, no. 2 (2007), 610--625.

arXiv math.GM/0601059 and HAL ccsd-00016422

This paper, solving the 60-year old Congruence Lattice Problem traditionally attributed to R.P. Dilworth, was received by J. Amer. Math. Soc. on January 26, 2006. On December 5, 2006, the paper was rejected, not taking into account the positive referees' reports. The rejection letter, quite a model of academic hypocrisy, can be seen here (with name of the handling editor edited out).

See also the following Wikipedia article. The following survey article, written by George Grätzer, Two Problems That Shaped a Century of Lattice Theory, Notices Amer. Math. Soc. 54, no. 6 (2007), 696--707, partly deals with the Congruence Lattice Problem.

In relation with these matters, read the Letters to the Editors section in the abovecited issue of Notices Amer. Math. Soc., and don't miss the essay by Doron Zeilberger, Because You Snubbed Others You Were Snubbed, and Those Who Snubbed You Shall Be Snubbed.

Also, read Melvin Henriksen's most interesting essay, There are too many B.A.D. mathematicians (reprinted from The Mathematical Intelligencer, volume 15, no. 1 (1993)), more and more relevant as time goes.

Related material: read the article by Joseph F. Grcar, Topical Bias in Generalist Mathematics Journals, The Mathematical Intelligencer, volume 57, no. 11 (December 2010)

[69] Finitely generated antisymmetric graph monoids,

P. Ara, F. Perera, and F. Wehrung, Journal of Algebra 320, no. 5 (1 September 2008), 1963--1982.

HAL ccsd-00156906

[70] Embedding coproducts of partition lattices,

F. Wehrung, Acta Sci. Math. (Szeged) 73, no. 3-4 (2007), 429--443.

arXiv 0709.4469 and HAL ccsd-00175368

[71] Embedding properties of endomorphism semigroups,

J. Araújo and F. Wehrung, Fundamenta Mathematicae 202, no. 2 (2009), 125--146.

arXiv 0801.2644 and HAL ccsd-00206738

[72] Large semilattices of breadth three,

F. Wehrung, Fundamenta Mathematicae 208, no. 1 (2010), 1--21.

arXiv 0804.1781 and HAL ccsd-00272111

[73] An infinite combinatorial statement with a poset parameter,

P. Gillibert and F. Wehrung, Combinatorica 31, no. 2 (2011), 183--200.

arXiv 0902.4448 and HAL-00364329

[74] Coordinatization of lattices by regular rings without unit and Banaschewski functions,

F. Wehrung, Algebra Universalis 64, no. 1 (2010), 49--67.

arXiv 0903.4756 and HAL-00371268

[75] From objects to diagrams for ranges of functors,

P. Gillibert and F. Wehrung, x+158 pages, Springer Lecture Notes in Mathematics Vol. 2029, 2011.

arXiv 1003.4850 and HAL-00462941

[76] A non-coordinatizable sectionally complemented modular lattice with a large Jónsson four-frame,

F. Wehrung, Advances in Applied Mathematics 47, no. 1 (July 2011), 173--193.

arXiv 1003.5158 and HAL-00462951.

[77] Infinite combinatorial issues raised by lifting problems in universal algebra,

F. Wehrung, Order 29, no. 2 (2012), 381--404.

arXiv 1009.0949 and HAL-00509814

[78] Lifting defects for nonstable K₀-theory of exchange rings and C*-algebras,

F. Wehrung, Algebras and Representation Theory 16, no. 2 (2013), 553--589.

arXiv 1101.4803 and HAL-00559268

[79] Varieties of lattices with geometric descriptions,

L. Santocanale and F. Wehrung, Order 30, no. 1 (2013), 13--38.

arXiv 1102.2195 and HAL-00564024

[80] Sublattices of associahedra and permutohedra,

L. Santocanale and F. Wehrung, Advances in Applied Mathematics 51, no. 3 (2013), 419--445.

arXiv 1103.3488 and HAL-00564024

[81] The extended permutohedron on a transitive binary relation,

L. Santocanale and F. Wehrung, European Journal of Combinatorics 42 (November 2014), 179--206.

arXiv 1211.2301 and HAL-00750265

[82] Lattices of regular closed subsets of closure spaces,

L. Santocanale and F. Wehrung, International Journal of Algebra and Computation 24, no. 7 (2014), 969--1030.

arXiv 1307.1480 and HAL-00836420

[83] The equational theory of the weak Bruhat order on finite symmetric groups,

L. Santocanale and F. Wehrung, Journal of the European Mathematical Society 20, no. 8 (2018), 1959--2003.

HAL-00986148

[84] Refinement monoids, equidecomposability types, and Boolean inverse semigroups,

F. Wehrung,

Springer Lecture Notes in Mathematics number 2188.

HAL-01197354

[85] Relative projectivity and transferability for partial lattices,

F. Wehrung, Order 35, no. 1 (March 2018), pp 111--132, SharedIt access

HAL-01222118, arXiv 1612.04189.

[86] Gcd-monoids arising from homotopy groupoids,

F. Wehrung, Semigroup Forum 97, no. 3 (December 2018), 493--522. SharedIt access

arXiv 1712.02787 and HAL-01338106

[87] Multifraction reduction III: the case of interval monoids,

P. Dehornoy and F. Wehrung, Journal of Combinatorial Algebra 1, no. 4 (2017), 341--370,

arXiv 1606.09018 and HAL-01338434.

[88] Varieties of Boolean inverse semigroups,

F. Wehrung, Journal of Algebra 511, 1 October 2018, Pages 114--147. Shared link (until August 29, 2018)

arXiv 1610.07447 and HAL-01386827

[89] Spectral spaces of countable Abelian lattice-ordered groups,

F. Wehrung, Transactions of the American Mathematical Society 371, no. 3 (February 2019), 2133--2158.

arXiv 1701.03494 and HAL-01431444

[90] Real spectrum versus l-spectrum via Brumfiel spectrum,

F. Wehrung, Algebras and Representation Theory26 (2023), 137--158. SharedIt access

arXiv 1706.09802 and HAL-01550450

[91] Ranges of functors in algebra,

F. Wehrung, The Mathematics Student 87, Nos. 1-2, January-June 2018, 67--81.

HAL-01856245

[92] Cevian operations on distributive lattices,

F. Wehrung, Journal of Pure and Applied Algebra 224, no. 4 (April 2020), 106202. Shared link (until December 12, 2019)

HAL-01988169

[93] From non-commutative diagrams to anti-elementary classes,

F. Wehrung, 56 pages, Journal of Mathematical Logic 21, no. 2 (2021), 2150011.

HAL-02000602

[94] Real spectra and l-spectra of algebras and vector lattices over countable fields,

F. Wehrung, 25 pages, Journal of Pure and Applied Algebra 226, no. 4 (April 2022), 106861. Shared link (until October 6, 2021)

HAL-02179699

[95] Right-orderability versus left-orderability for monoids,

F. Wehrung, Semigroup Forum 102, no. 3 (2021), 885--899.

HAL-02872310 SharedIt access

[96] Projective classes as images of accessible functors,

F. Wehrung, Journal of Logic and Computation 33, no. 1 (January 2023), 90--135.

HAL-03580184

[97] Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one,

M. Ploščica and F. Wehrung, Acta Sci. Math. (Szeged) 89, no. 3-4 (2023), 339--356. SharedIt link.

HAL-03696927

[98] A solution to the MV-spectrum Problem in size aleph one,

M. Ploščica and F. Wehrung,

HAL-04040959, J. Algebra 640 (15 February 2024), 253--273. Shared link (until January 1, 2024)

[99] Monotone-Cevian and finitely separable lattices,

M. Ploščica and F. Wehrung, 18 pages,

HAL-04228820