On residual finiteness of direct products of algebraic systems

Gray, R and Ruskuc, N (2009) On residual finiteness of direct products of algebraic systems. Monatshefte für Mathematik, 158 (1). pp. 63-69. ISSN 0026-9255

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Abstract

It is well known that if two algebraic structures A and B are residually finite then so is their direct product. Here we discuss the converse of this statement. It is of course true if A and B contain idempotents, which covers the case of groups, rings, etc. We prove that the converse also holds for semigroups even though they need not have idempotents. We also exhibit three examples which show that the converse does not hold in general.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Users 2731 not found.
Date Deposited:	21 Feb 2013 22:20
Last Modified:	07 Nov 2024 12:33
URI:	https://ueaeprints.uea.ac.uk/id/eprint/41520
DOI:	10.1007/s00605-008-0036-4

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