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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

Cresp, J. and Sullivan, R. P. (1975), ‘Semigroups in rings’, J. Austral. Math. Soc. (Ser. A), 20, 172–177.CrossRefGoogle Scholar
Kist, J. (1963), ‘Minimal prime ideals in commutative semigroups’, Proc. London Math. Soc. (3) 13, 31–50.CrossRefGoogle Scholar
Ligh, Steve (1978), ‘A note on semigroups in rings’, J. Austral. Math. Soc. (Ser. A.), 25, 305–308.Google Scholar
Martindale, W. S. III (1969), ‘When are multiplicative mappings additive?’, Proc. Amer. Math. Soc. 21, 695–698.Google Scholar
Warner, S. (1971), Classical modern algebra (Prentice-Hall, Englewood Cliffs, New Jersey).Google Scholar