A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier) Original Research Article

Recently, Craig Squier introduced the notion of finite derivation type to show that some finitely presentable monoid has no presentation by means of a finite complete rewriting system. A similar result was already obtained by the same author using homology, but the new method is more direct and more powerful. Here, we present Squierʹs argument with a bit of categorical machinery, making proofs shorter and easier. In addition we prove that if a monoid has finite derivation type, then its third homology group is of finite type.