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Orthodox semirings and rings

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

John Zeleznikow
John Zeleznikow
Affiliation:
Department of Mathematicx, Monash University, Clayton, Victoria 3168, Australia
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Abstract

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We show that in a regular ring (R, +, ·), with idempotent set E, the following conditions are equivalent: (i) (ii) (R, ·) is orthodox. (iii) (R, ·) is a semilattice of groups. These and other conditions are also considered for regular semigroups, and for semirings (S, +, · ), in which (S, +) is an inverse semigroup. Examples are given to show that they are not equivalent in these cases.

MSC classification

Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 50 - 54
Copyright
Copyright © Australian Mathematical Society 1980

References

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