A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier) (Q1892306)

The paper deals with Squier's arguments on finite derivation type [\textit{C. C. Squier}, J. Pure Appl. Algebra 49, 201-217 (1987; Zbl 0648.20045); \textit{C. C. Squier} and \textit{F. Otto}, Lect. Notes Comput. Sci. 256, 74-82 (1987; Zbl 0625.03023)]. Proofs are made shorter and easier by categorical machinery. Squier's finiteness condition is of invariant type. It can be defined in terms of a finite presentation, but does not depend on the choice of this presentation. The result is that if a monoid has finite derivation type, then its third homology group is of finite type.