C. Les-Éléments-de, . Soit-f:-c-?-l-le-plongement-canonique, ?. Soit-k, ?. .. {0, and . 1}, Nous avons x k ? x k+1 , donc ? L (x k , x k+1 ) est sup-irréductible dans Con c L, Comme Con c L est booléen, ? L (x k , x k+1 ) est un atome de Con c L. Soit ? un atome de Con c L, nous avons : ? ? ? L (0, 1) = m?1 k=0 ? L (x k

?. Donc-il-existe-k and . {0, m ? 1} tel que ? ? ? L (x k , x k+1 ) Mais ? L (x k , x k+1 ) est un atome de Con c L, d'où ? = ? L (x k , x k+1 ) Donc Con c f est surjective

. Comme-lh-(-k-)->-n, nous pouvons supposer que 0 et 1 sont dans C) Soit f : C ? K l'injection canonique Supposons que g : C ? ? K ? soit un relèvement de Con c f dans V 2 Comme f est injective, g est aussi injectiveC ? ) = n + 1. D'où n ? lh(K ? ) ? lh(C ? ) = n + 1 ; une contradiction

G. Birkhoff, Lattice Theory, 1961.
DOI : 10.1090/coll/025

S. Bulman-fleming and K. Mcdowell, Flat semilattices, Proceedings of the American Mathematical Society, vol.72, issue.2, pp.228-232, 1978.
DOI : 10.1090/S0002-9939-1978-0505915-X

S. Z. Ditor, Cardinality questions concerning semilattices of finite breadth, Discrete Math, pp.47-59, 1984.

B. A. Davey and B. Sands, An application of Whitman's condition to lattices with no infinite chains, Algebra Universalis, vol.42, issue.1, pp.171-178, 1977.
DOI : 10.1007/BF02485426

P. Erdös, A. Hajnal, A. Máté, and R. Rado, Combinatorial Set Theory : Partition Relations for Cardinals, Studies in Logic and the Foundations of Mathematics, 1984.

C. Faith and Y. Utumi, On a new proof of Litoff's theorem, Acta Mathematica Academiae Scientiarum Hungaricae, vol.69, issue.3-4, pp.369-371, 1963.
DOI : 10.1007/BF01895723

R. Freese, W. A. Lampe, and W. Taylor, Congruence lattices of algebras of fixed similarity type. I, Pacific, J. Math, vol.82, issue.1, pp.59-68, 1979.

K. D. Fryer and I. Halperin, Coordinates in geometry, Trans. Roy. Soc. Canada. Sect. III, issue.3, pp.48-59, 1954.

N. Funayama and T. Nakayama, On the distributivity of a lattice of lattice-congruences, Proc. Imp. Acad. Tokyo, pp.553-554, 1942.
DOI : 10.3792/pia/1195573786

G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove et al., A Compendium of Continuous Lattices, 1980.
DOI : 10.1007/978-3-642-67678-9

P. Gillibert, Critical points of pairs of varieties of algebras, préprint, Internat. J. Algebra Comput, 2007.

P. Gillibert, Critical points between varieties generated by subspace lattices of vector spaces, préprint, 2008.

G. Grätzer, B. A. Davey, R. Freese, B. Ganter, M. Greferath et al., General Lattice Theory, 1998.

C. Herrmann, Generators for Complemented Modular Lattices and the von-Neumann-Jónsson Coordinatization Theorems, préprint, 2008.

G. Grätzer and E. T. Schmidt, On congruence lattices of lattices, Acta Mathematica Academiae Scientiarum Hungaricae, vol.9, issue.1-2, pp.179-185, 1962.
DOI : 10.1007/BF02033636

G. Grätzer and E. T. Schmidt, Characterizations of congruence lattices of abstract algebras, Acta Sci. Math. (Szeged), vol.24, pp.34-59, 1963.

G. Grätzer, H. Lakser, and F. Wehrung, Congruence amalgamation of lattices, Acta Sci. Math. (Szeged), vol.66, issue.12, pp.3-22, 2000.

K. R. Robert and E. , Von Neumann Regular Rings, 1991.

A. Hajnal and A. Máté, Set Mappings, Partitions, and Chromatic Numbers, Studies in Logic and the Foundations of Mathematics, vol.80, pp.347-379, 1973.
DOI : 10.1016/S0049-237X(08)71956-6

A. P. Huhn, On the representation of distributive algebraic lattices, III. Acta Sci. Math. (Szeged), vol.53, issue.12, pp.11-18, 1989.

P. Jipsen and H. Rose, Varieties of lattices, Lecture Notes in Mathematics, vol.1533, 1992.

B. Jónsson, Representations of Relatively Complemented Modular Lattices, Transactions of the American Mathematical Society, vol.103, issue.2, pp.272-302, 1962.
DOI : 10.2307/1993660

B. Jónsson, Algebras Whose Congruence Lattices are Distributive., MATHEMATICA SCANDINAVICA, vol.21, pp.110-121, 1967.
DOI : 10.7146/math.scand.a-10850

C. Kuratowski, Sur une caractérisation des alephs, Fund, Math, vol.38, pp.14-17, 1951.

W. A. Lampe, Congruence lattices of algebras of fixed similarity type. II, Pacific Journal of Mathematics, vol.103, issue.2, pp.475-508, 1982.
DOI : 10.2140/pjm.1982.103.475

W. A. Lampe, Simultaneous congruence representations: a special case, Algebra universalis, vol.54, issue.2, pp.249-255, 2005.
DOI : 10.1007/s00012-005-1931-3

M. Plo??ica, Separation properties in congruence lattices of lattices, Colloq. Math, vol.83, pp.71-84, 2000.

M. Plo??ica, Dual spaces of some congruence lattices, Topology and its Applications, vol.131, issue.1, pp.1-14, 2003.
DOI : 10.1016/S0166-8641(02)00259-6

M. Plo??ica, Nonrepresentable distributive semilattices, J. Pure Appl. Algebra

M. Plo??ica, J. T?ma, and F. Wehrung, Congruence lattices of free lattices in nondistributive varieties, Colloq. Math, vol.76, issue.2, pp.269-278, 1998.

P. Pudlák, On congruence lattices of lattices, Algebra Universalis, vol.20, issue.1, pp.96-114, 1985.
DOI : 10.1007/BF01236809

P. R??i?ka, Free trees and the optimal bound in Wehrung's theorem, Fundamenta Mathematicae, vol.198, issue.3, pp.217-228, 2008.
DOI : 10.4064/fm198-3-2

P. R??i?ka, J. T?ma, and F. Wehrung, Distributive congruence lattices of congruence-permutable algebras, Journal of Algebra, vol.311, issue.1, pp.96-116, 2007.
DOI : 10.1016/j.jalgebra.2006.11.005

E. T. Schmidt, Every finite distributive lattice is the congruence lattice of some modular lattice, Algebra Universalis, vol.18, issue.1, pp.49-57, 1974.
DOI : 10.1007/BF02485706

E. T. Schmidt, The ideal lattice of a distributive lattice with 0 is the congruence lattice of a lattice, Acta Sci. Math. (Szeged), vol.43, issue.12, pp.153-168, 1981.

J. T?ma and F. Wehrung, A survey of recent results on congruence lattices of lattices, Algebra Universalis, vol.48, issue.4, pp.439-471, 2002.
DOI : 10.1007/s000120200011

F. Wehrung, The dimension monoid of a lattice, Algebra Universalis 40, pp.247-411, 1998.

F. Wehrung, A uniform refinement property for congruence lattices, Proceedings of the American Mathematical Society, vol.127, issue.02, pp.363-370, 1999.
DOI : 10.1090/S0002-9939-99-04558-X
URL : https://hal.archives-ouvertes.fr/hal-00004063

F. Wehrung, A solution to Dilworth's congruence lattice problem, Advances in Mathematics, vol.216, issue.2, pp.610-625, 2007.
DOI : 10.1016/j.aim.2007.05.016