Journal of the Australian Mathematical Society (Series A)

Research Article

Semirings with a completely simple additive semigroup

Mireille P. Grilleta1

a1 c/o Pierre A. Grillet Tulane University New Orleans, La 70118, U.S.A.

We construct all semirings with a given completely simple additive semiroup xs2133(G, I, xs2227, P) by means of an associative and distributive multiplication on G, and associative multiplications on I and xs2227 satisfying certain conditions.

(Received February 26 1973)

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. [OpenURL Query Data]  [Google Scholar]