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Journal of the London Mathematical Society 1996 53(1):79-98; doi:10.1112/jlms/53.1.79
© 1996 by London Mathematical Society
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© The London Mathematical Society

The Word Problem in the Variety of Inverse Semigroups with Abélian Covers

John Meakin and Mark Sapir

Department of Mathematics, University of Nebraska at Lincoln Lincoln, NE 68588, USA

Received 1 October 1993. Revision received 1 June 1994.

The variety of inverse semigroups which possess E-unitary covers over Abelian groups coincides with the Mal'cev product of the variety of semilattices and the variety of Abelian groups,and also with the variety generated by semidirect products of semilattices and Abelian groups. We show that this variety (and any variety of inverse semigroups that contains this variety) has undecidable word problem.

Research of both authors supported by NSF Grant DMS-9203981 and by the Center for Communication and Information Science, University of Nebraska at Lincoln.


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