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Fragmented rings

Published online by Cambridge University Press:  14 November 2011

Paul Dubreil
Paul Dubreil
Affiliation:
Université de Paris VI
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Synopsis

The publication of the results in this paper has been delayed, for non-mathematical reasons. However, the author has given lectures on these results in Smolenice [2], Gainesville, Tulane. Riverside (1971), Milan (1972) and in Paris. The main consideration in this paper is the notion of a fragmented ring and its multiplicative semigroup. A fragmented ring is a ring with an identity having a finite set of idempotents, these commuting and therefore being central. In a subsequent paper we shall consider associated ideas in a purely semigroup-theoretic context and, in so doing, point out some differences between general semigroups and those semigroups that are the multiplicative semigroups of rings.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 78 , Issue 3-4 , 1978 , pp. 273 - 283
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

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