Finiteness properties of direct products of algebraic structures

P. Mayr, Nikola Ruskuc

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)167-187
Number of pages21
JournalJournal of Algebra
Volume494
Early online date3 Nov 2017
DOIs
Publication statusPublished - 15 Jan 2018

Keywords

  • Finitely generated
  • Finitely presented
  • Residual finite

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