Abstract
AbstractWe show that rings for which every non-constant multiplicative endomorphism is additive are trivial or power rings (that is, rings R such that R = R2 and x2 = 0 = x+x for all x ∈ R) and that if R is a power ring for which every multiplicative endomorphism is additive, then End (R) is a zero semigroup or a semilattice according to how the product is defined.
Publisher
Cambridge University Press (CUP)
Cited by
2 articles.
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1. Associative rings;Journal of Soviet Mathematics;1987-08
2. Rings satisfying certain conditions either on subsemigroups or on endomorphisms;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1986-04