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The embeddability of ring and semigroup amalgams is undecidable

Part of: Semigroups General and miscellaneous

Published online by Cambridge University Press:  09 April 2009

Marcel Jackson
Marcel Jackson
Affiliation:
Discipline of Mathematics University of TasmaniaGPO Box 252-37 Hobart 7001Australia email: marcel_j@hilbert.maths.utas.edu.au Department of Mathematics La Trobe UniversityBundoora VIC 3083Australia e-mail: m.g.jackson@latrobe.edu.au
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Abstract

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We prove that there is no algorithm to determine when an amalgam of finite rings (or semigroups) can be embedded in the class of rings or in the class of finite rings (respectively, in the class of semigroups or in the class of finite semigroups). These results are in marked contrast with the corresponding problems for groups where every amalgam of finite groups can be embedded in a finite group.

MSC classification

Secondary: 16B99: None of the above, but in this section 20M99: None of the above, but in this section 20M25: Semigroup rings, multiplicative semigroups of rings 20M05: Free semigroups, generators and relations, word problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 69 , Issue 2 , October 2000 , pp. 272 - 286
Copyright
Copyright © Australian Mathematical Society 2000

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