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Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/2146
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Title: On residual finiteness of direct products of algebraic systems
Authors: Gray, R.
Ruskuc, Nik
Keywords: Residual finiteness
Direct product
Semigroup
Unary algebra
QA Mathematics
Issue Date: Sep-2009
Citation: Gray , R & Ruskuc , N 2009 , ' On residual finiteness of direct products of algebraic systems ' Monatshefte für Mathematik , vol 158 , no. 1 , pp. 63-69 .
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.
Version: Postprint
Status: Peer reviewed
URI: http://hdl.handle.net/10023/2146
DOI: http://dx.doi.org/10.1007/s00605-008-0036-4
ISSN: 0026-9255
Type: Journal article
Rights: This is an author version of this article. The original publication (c) Springer-Verlag 2008 is available at www.springerlink.com
Appears in Collections:Mathematics & Statistics Research
University of St Andrews Research
Pure Mathematics Research



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