A new finiteness condition for monoids presented by complete rewriting systems (after Craig C. Squier). (English) Zbl 0832.20080

The paper deals with Squier’s arguments on finite derivation type [C. C. Squier, J. Pure Appl. Algebra 49, 201-217 (1987; Zbl 0648.20045); C. C. Squier and 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.


20M05 Free semigroups, generators and relations, word problems
20M35 Semigroups in automata theory, linguistics, etc.
20M50 Connections of semigroups with homological algebra and category theory
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