Boolean factor Congruences and Property (*)

TitleBoolean factor Congruences and Property (*)
Publication TypeJournal Article
Year of Publication2011
AuthorsSánchez Terraf, P
JournalInternational Journal of Algebra and Computation
AbstractA variety V has Boolean factor congruences (BFC) if the set of factor congruences of any algebra in V is a distributive sublattice of its congruence lattice; this property holds in rings with unit and in every variety which has a semilattice operation. BFC has a prominent role in the study of uniqueness of direct product representations of algebras, since it is a strengthening of the refinement property. We provide an explicit Mal'cev condition for BFC. With the aid of this condition, it is shown that BFC is equivalent to a variant of the definability property (*), an open problem in Willard's work[9].
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