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- W1966641840 abstract "The family ( R ) of all endomorphisms of a ring R is a semigroup under composition. It follows easily that if R and T are isomorphic rings, then ( R ) and (T) are isomorphic semigroups. We devote ourselves here to the converse question: ‘If ( R ) and ( T ) are isomorphic, must R and T be isomorphic?’ As one might expect, the answer is, in general, negative. For example, the ring of integers has precisely two endomorphisms – the zero endomorphism and the identity automorphism. Since the same is true of the ring of rational numbers, the two endomorphism semigroups are isomorphic while the rings themselves are certainly not." @default.
- W1966641840 created "2016-06-24" @default.
- W1966641840 creator A5016416171 @default.
- W1966641840 date "1970-11-01" @default.
- W1966641840 modified "2023-09-23" @default.
- W1966641840 title "The semigroup of endomorphisms of a Boolean ring" @default.
- W1966641840 cites W1976663252 @default.
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- W1966641840 doi "https://doi.org/10.1017/s1446788700007886" @default.
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