On residual finiteness of direct products of algebraic systems

R. Gray; Nik Ruskuc

doi:10.1007/s00605-008-0036-4

On residual finiteness of direct products of algebraic systems

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	63-69
Number of pages	7
Journal	Monatshefte für Mathematik
Volume	158
Issue number	1
Early online date	13 Aug 2008
DOIs	https://doi.org/10.1007/s00605-008-0036-4
Publication status	Published - Sept 2009

Keywords

Residual finiteness
Direct product
Semigroup
Unary algebra

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10.1007/s00605-008-0036-4

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This is an author version of this article. The original publication (c) Springer-Verlag 2008 is available at www.springerlink.com
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Cite this

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On residual finiteness of direct products of algebraic systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Cite this

On residual finiteness of direct products of algebraic systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Finiteness Conditions and Index: Finiteness Conditions and Index in Semigroups and Monoids

EP/C523229/1: Multidisciplinary Critical Mass in Computational Algebra and Applications

Cite this