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A note on semigroups in rings

Published online by Cambridge University Press:  09 April 2009

Steve Ligh
Steve Ligh
Affiliation:
Department of Mathematics, University of Southwestern Louisiana, Lafayette, Louisiana, USA.
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Recently J. Cresp and R. P. Sullivan (1975) investigated those rings R with the following properties: (*) every multiplicative subsemigroup of R is a subring. (**) every multiplicative subsemigroup of R containing 0 is a subring. For rings with (*) they obtained the following characterization.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 305 - 308
Copyright
Copyright © Australian Mathematical Society 1977

References

Cresp, J. and Sullivan, R. P. (1975), ‘Semigroups in rings’, J. Austral. Math. Soc. 20, 172–177.Google Scholar
Gluskin, L. M. (1963), ‘Ideals in rings and their multiplicative semigroups’, Uspedni Mat. Nauk. (N. S.) 15, 4 (94), 141–148; translated in Amer. Math. Soc. Translations, 27 (2) 297–304.Google Scholar
Ligh, Steve (1969), “On boolean near-rings”, Bull. Austral. Math. Soc. 1, 375–379.CrossRefGoogle Scholar
Ligh, Steve, McQuarrie, Bruce and Slotterbeck, Oberta (1972), ‘On near-fields’, J. London Math. Soc. (2) 5, 87–90.Google Scholar
Ligh, Steve and Neal, Larry (1974), ‘A note on Mersenne numbers’, Math. Magazine 47, 231–233.CrossRefGoogle Scholar