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Lecture Notes in Computer Science
The main purpose of this paper is to describe a negative answer to the following question: Does every finitely presented monoid with a decidable word problem have a presentation (~;R) where R is a finite canonical rewriting system? To obtain this answer a certain homological finiteness condition for monoids is considered. If M is a monoid that can be presented by a finite canonical rewriting system, then M is an (FP)3-monoid. Since there are well-known examples of finitely presented groups thatdoi:10.1007/3-540-17220-3_7 fatcat:7chzcveea5a5feprziyku25vyu