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Rings satisfying certain conditions either on subsemigroups or on endomorphisms

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

A. Cherubini  and
A. Varisco
A. Cherubini
Affiliation:
Dipartimento di Matematica, Politecmco di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
A. Varisco
Affiliation:
Dipartimento di Matematica, Politecmco di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
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Abstract

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We characterize rings whose multiplicative subsemigroups containing 0 and the additive inverse of each element are subrings. In addition we consider commutative rings for which every non-constant multiplicative endormorphism that preserves additive inverses is a ring endomorphism, and we show that they belong to one of three easily-described classes of rings.

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 194 - 202
Copyright
Copyright Australian Mathematical Society 1986

References

1Chacron, M., On a theorem of Herstein, Canad. J. Math 21 (1969), 13481353.CrossRefGoogle Scholar
2Cherubini, A. and Varisco, A., On Putcha's Q-semigroups, Semigroup Forum 18 (1979), 313317.Google Scholar
3Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups (Amer. Math. Soc., Providence, R. I., Vol. 1, 1961).Google Scholar
4Cresp, J. and Sullivan, R. P., Semigroups in rings, J. Austral. Math. Soc. (Ser. A) 20 (1969), 172177.CrossRefGoogle Scholar
5Duncan, J. and Macdonald, I. D., Some factorable nil rings of characteristic two, Proc. Roy. Soc. Edinburgh Sect. A, 82 (1979), 193199.CrossRefGoogle Scholar
6Herstein, I. N., The structure of a certain class of rings, Amer. J. Math. 75 (1953), 864871.CrossRefGoogle Scholar
7Hirano, Y. and Tominaga, H., On rings whose non-constant semigroup endormorphisms are ring endomorphisms, Math. J. Okayama Univ. 23 (1981), 1316.Google Scholar
8Ligh, S., On a class of semigroups admitting ring structure, Semigroup Forum 13 (1976), 3746.CrossRefGoogle Scholar
9Ligh, S., A note on semigroups in rings, J. Austral. Math. Soc. (Ser. A) 24 (1977), 305308.CrossRefGoogle Scholar
10Putcha, M. S., Semilattice decompositions of semigroups, Semigroup Forum 6 (1973), 1234.CrossRefGoogle Scholar
11Sullivan, R. P., Semigroup endomorphisms of rings, J. Austral. Math. Soc. (Ser. A) 26 (1978), 319322.CrossRefGoogle Scholar