Finiteness properties of direct products of algebraic structures

We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include Mal'cev algebras (including groups, rings and other cla...

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Bibliographic Details
Published inJournal of algebra Vol. 494; pp. 167 - 187
Main Authors Mayr, Peter, Ruškuc, Nik
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.01.2018
Subjects
Finitely generated
Finitely presented
Residual finite
secondary
Finitely generated
Finitely presented
primary
Residual finite
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Summary:We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types of algebraic structures. The structures considered include Mal'cev algebras (including groups, rings and other classical algebras, as well as loops), idempotent algebras (including lattices), semigroups, and algebras in congruence modular varieties. We aim to identify as broad classes as possible in which the ‘expected’ preservation results (A×B satisfies property P if and only if A and B satisfy P) hold, and to exhibit ways in which they may fail outside those classes.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.09.035