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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

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