On semigroups admitting ring structure

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. Communicated by A. H. Clifford