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Semigroup endomorphisms of rings

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

R. P. Sullivan
R. P. Sullivan
Affiliation:
University of Western Australia Nedlands 6009 Australia
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Abstract

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We 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.

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 3 , November 1978 , pp. 319 - 322
Copyright
Copyright © Australian Mathematical Society 1978

References

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