Minimal sequences in semigroups

Putcha, Mohan S.

doi:10.1090/S0002-9947-1974-0338233-4

Minimal sequences in semigroups
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by Mohan S. Putcha

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

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

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Abstract:

In this paper we generalize a result of Tamura on $\delta$-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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