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Semigroups in Which all Subsemigroups are Left Ideals

Published online by Cambridge University Press:  20 November 2018

Naoki Kimura ,
Takayuki Tamura  and
Rudolph Merkel
Naoki Kimura
Affiliation:
University of Saskatchewan
Takayuki Tamura
Affiliation:
University of Oklahoma
Rudolph Merkel
Affiliation:
University of California, Davis
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A semigroup S is a λ- [ρ-, σ-] semigroup if and only if each subsemigroup of S is a left [right, two-sided] ideal of S. Since the concept of ρ-semigroup is the dual of that of λ-semigroup, the results for ρ-semigroups are generally not stated explicitly, σ-semigroups are treated as a special case of λ-semigroups ; in fact, a semigroup S is a σ-semigroup if and only if it is a λ-semigroup and a ρ-semigroup. The purpose of this paper is to determine the structure of λ- [ρ-, σ-] semigroups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 52 - 62
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups (Providence, 1961).Google Scholar