On semigroups admitting ring structure II |
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Authors: | M Satyanarayana |
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Institution: | (1) Bowling Green State University, 43403 Bowling Green, Ohio |
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Abstract: | We shall consider semigroups with O, which contain a unique maximal right ideal generated by a finite number of independent
generators and in which every proper right ideal is contained in the unique maximal right ideal and investigate when these
semigroups are multiplicative semigroups of a ring. We prove in particular that the necessary condition for this class of
semigroups S to admit ring structure is S=S2 if |S|>2. Furthermore the admissible ring structure of S is determined when the product of every two generators of the maximal
right ideal M is O and when S satisfies one of the two conditions, namely S is commutative without idempotents except O and
1 or every generator of M is nilpotent. |
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Keywords: | |
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