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| Title: | On residual finiteness of direct products of algebraic systems |
| Authors: | Gray, R.
Ruskuc, N. |
| 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: | University of St Andrews Research
Pure Mathematics Research
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