Algorithmic problems for amalgams of finite semigroups
type: Item
instance of: scholarly article
title: Algorithmic problems for amalgams of finite semigroups
zbMATH Open document ID: 0959.20050
author: Mark Sapir
published in: Journal of Algebra
publication date: 2000-11-19T00:00:00Z
review text: It is proved that there is an amalgam of two finite semigroups such that the corresponding amalgamated product has an undecidable word problem. Further, both the problems of embeddability of finite semigroup amalgams in arbitrary semigroups and into finite semigroups are undecidable. Moreover, the finite semigroups involved can be taken to have the property that all products of length four equal zero. The proofs use several versions of Minsky algorithms (one type of which consists of a numbered sequence of instructions for passing coins between two glasses) and a result of Slobodskoj's about undecidability of the universal theory of finite groups. The reader should note that the article was reprinted because of a typesetting error in the original which caused referencing to be omitted: the complete version is in ibid. 232, 767-785 (2000).
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 1502162
zbMATH Keywords: finite semigroups
zbMATH Keywords: amalgamated products
zbMATH Keywords: undecidable word problem
zbMATH Keywords: embeddability of finite semigroup amalgams
zbMATH Keywords: Minsky algorithms
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
full work available at URL: jabr.1999.8138
OpenAlex ID: W1972395679
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DOI: 10.1006/JABR.1999.8138
DOI: 10.1006/JABR.2000.8559
description: scientific article; zbMATH DE number 1502162