On residual finiteness of direct products of algebraic systems

R. Gray, Nik Ruskuc

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)63-69
Number of pages7
JournalMonatshefte für Mathematik
Issue number1
Early online date13 Aug 2008
Publication statusPublished - Sept 2009


  • Residual finiteness
  • Direct product
  • Semigroup
  • Unary algebra


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