CIEM 05476
CENTRO DE INVESTIGACION Y ESTUDIOS DE MATEMATICA
Unidad Ejecutora - UE
artículos
Título:
Boolean Factor Congruences and Property (*)
Autor/es:
PEDRO SÁNCHEZ TERRAF
Revista:
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Editorial:
WORLD SCIENTIFIC PUBL CO PTE LTD
Referencias:
Año: 2011 vol. 21 p. 931 - 950
ISSN:
0218-1967
Resumen:
A variety V has Boolean factor congruences (BFC) if the set of factor congruences of every 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 R. Willard´s work ("Varieties Having Boolean Factor Congruences," J. Algebra, 132 (1990)).
