Varieties having Boolean factor congruences
نویسندگان
چکیده
منابع مشابه
Varieties Having Boolean Factor Congruences
Every ring R with identity satisfies the following property: the factor ideals of R (i.e., those ideals I such that I+ J= R and In J= (0) for some ideal J) form a Boolean sublattice of the lattice of all ideals of R. The universal algebraic abstraction of this property is known as Boolean factor congruences (BFC) or as the strict refinement property; more examples of algebras having BFC are lat...
متن کاملBoolean factor Congruences and Property (*)
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 refineme...
متن کاملVarieties with Definable Factor Congruences
We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are definable in a first-orderlogic sense, among them the concept of Definable Factor Congruences (DFC). The main results are that DFC is a Mal’cev property and that it is equivalent to all other conditions formulated; in particular we prove that V has DFC if and...
متن کاملBoolean Metric Spaces and Boolean Algebraic Varieties
The concepts of Boolean metric space and convex combination are used to characterize polynomial maps An −→ Am in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to t...
متن کاملOn Solvable Congruences in Finitely Decidable Varieties
In this paper we establish the (1, 2) and (2, 1)-transfer principles for finitely decidable locally finite varieties. A class of structures is finitely decidable if the first order theory of its finite members is recursive. A variety is a class of algebras which is axiomatizable by a set of equations. The transfer principles deal with the local structure of finite algebras and have strong globa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90257-o