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On semigroups of endomorphisms of generalized Boolean rings

Published online by Cambridge University Press:  09 April 2009

Douglas B. Smith Jr  and
Jiang Luh
Douglas B. Smith Jr
Affiliation:
USAF Academy, Colorado 80840, U.S.A.
Jiang Luh
Affiliation:
North Carolina State University at Raleigh 27607, U.S.A.
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Magill in [4] first proved that two Boolean rings are isomorphic if and only if their respective endomorphism semigroups are isomorphic. His proof, however, relied on topological techniques. More recently Maxson has published a proof of the above using purely algebraic techniques [5]. In this paper, structure theorems are given which allow us to extend the above result to the pk-rings of Foster [1]. As a special case, the result is shown to apply also to p-rings. An example is given to show that a further extension to J-rings is impossible.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 411 - 418
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Foster, A. L., ‘pk-rings and ring-logics’, Ann. Scu. Norm. Pisa 5 (1951), 279–300.Google Scholar
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