The catenary and tame degree in finitely generated commutative cancellative monoids. (English) Zbl 1117.20045

Chapman, S. T.; García-Sánchez, P. A.; Llena, D.; Ponomarenko, V.; Rosales, J. C.

Manuscr. Math. 120, No. 3, 253-264 (2006).

Let \(S\) be a commutative cancellative atomic monoid. The catenary degree and the tame degree of \(S\) are (somewhat technical) combinatorial invariants of \(S\) which describe the behavior of chains of factorizations in \(S\) (see for example, the book Non-unique factorizations. Algebraic, combinatorial and analytic theory by A. Geroldinger and F. Halter-Koch [Pure Appl. Math. 278. Boca Raton, FL: Chapman & Hall/CRC (2006; Zbl 1113.11002)]).
In this paper, the authors give methods to compute both invariants when \(S\) is finitely generated. These methods are based on the computation of a minimal presentation of \(S\), and there are algorithms to compute this. Several examples are given to illustrate the theory.

Reviewer: David F. Anderson (Knoxville)

MSC:

20M14	Commutative semigroups
20M05	Free semigroups, generators and relations, word problems
13A05	Divisibility and factorizations in commutative rings

Keywords:

factorizations; finitely generated monoids; catenary degrees; tame degrees; commutative cancellative monoids; minimal presentations; algorithms

Citations:

Zbl 1113.11002

Software:

GAP

References:

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