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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Extensions of algebraic systems

Author: Awad A. Iskander
Journal: Trans. Amer. Math. Soc. 281 (1984), 309-327
MSC: Primary 08B25; Secondary 03C05, 08A05
MathSciNet review: 719672
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Abstract: There are several generalizations to universal algebras of the notion "The group $ \mathfrak{A}$ is an extension of the group $ \mathfrak{B}$ by the group $ \mathfrak{C}$". In this paper we study three such generalizations and the corresponding products of classes of algebraic systems. Various results are presented. One such theorem characterizes the weakly congruence regular varieties admitting extensions of a particular sort. Another result gives, under a weak congruence permutability condition, an equational basis for the variety obtained by applying one such product to two other varieties.

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Keywords: Classes of algebraic systems, universal algebras, expansions, extensions, weakly congruence permutable varieties, weakly congruence regular varieties, predicates, terms, identities, varieties with ideals, admitting extensions
Article copyright: © Copyright 1984 American Mathematical Society

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