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Semirings with a completely simple additive semigroup

Published online by Cambridge University Press:  09 April 2009

Mireille P. Grillet
Mireille P. Grillet
Affiliation:
c/o Pierre A. GrilletTulane UniversityNew Orleans, La 70118, U.S.A.
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We construct all semirings with a given completely simple additive semiroup ℳ(G, I, ∧, P) by means of an associative and distributive multiplication on G, and associative multiplications on I and ∧ satisfying certain conditions.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 257 - 267
Copyright
Copyright © Australian Mathematical Society 1975

References

Clifford, A. H. and Preston, G. B. (1962), The algebraic theory of semigroups, Vol. 1, Math. Surveys, No. 7, (Amer. Math. Soc., Providence, R. I., 1962.)Google Scholar
Grillet, M. P. (1972), ‘Embedding problems in semiring theory’, J. Austral. Math. Soc. 22, 168–181.CrossRefGoogle Scholar