Abstract
A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal by single elements and semigroups which are generated by two independent generators and describes their structure. We also prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero.
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References
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Satyanarayana, M.,Principal right ideal semigroups, J. London Math. Soc. (to appear).
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Communicated by A. H. Clifford
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Satyanarayana, M. On semigroups admitting ring structure. Semigroup Forum 3, 43–50 (1971). https://doi.org/10.1007/BF02572940
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DOI: https://doi.org/10.1007/BF02572940