Minimal sequences in semigroups

Author:
Mohan S. Putcha

Journal:
Trans. Amer. Math. Soc. **189** (1974), 93-106

MSC:
Primary 20M10

MathSciNet review:
0338233

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we generalize a result of Tamura on -indecomposable semigroups. Based on this, the concept of a minimal sequence between two points, and from a point to another, is introduced. The relationship between two minimal sequences between the same points is studied. The rank of a semigroup *S* is defined to be the supremum of the lengths of the minimal sequences between points in *S*. The semirank of a semigroup *S* is defined to be the supremum of the lengths of the minimal sequences from a point to another in *S*. Rank and semirank are further studied.

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0338233-4

Keywords:
Semigroups,
semilattice decomposition,
minimal sequence,
rank

Article copyright:
© Copyright 1974
American Mathematical Society