A NEW FINITENESS CONDITION FOR MONOIDS PRESENTED BY COMPLETE REWRITING-SYSTEMS (AFTER CRAIG-C.-SQUIER)

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 Squier's 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.