Publication at Faculty of Mathematics and Physics |
2010
Abstract
We denote by Conc(A) the semilattice of all compact congruences of an algebra A. Given a variety V of algebras, we denote by Conc(V) the class of all semilattices isomorphic to Conc(A) for some A in V.
Given varieties V and W of algebras, the critical point of V under W, denoted by crit(V,W) is the smallest cardinality of a semilattice that belongs to Conc(V)-Conc(W). Let K and F be finite field such that card K > card F, let A (resp., B) be a vector space of dimension 3 on K (resp., F).
Denote by V (resp., W) the variety of lattices generated by the subspace lattice of A (resp., B), then crit(V,W) is aleph 2.