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Semigroup ideals in rings

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

David A. Hill
David A. Hill*
Affiliation:
Trinity CollegeDublin, Ireland and Universidad Nacional Experimental de Tachira San Cristobal, Venezuela
*
Instituto de Matematica Universidade Federal de Bahia Caetano Moura, 99, Federação 40000 Salvador, Bahia Brasil
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Abstract

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A ring R is called an l-ring (r-ring) in case R contains an indentity and every left (right) semigroup ideal is a left (right) ring ideal. A number of structure theorems are obtained for l-rings when R is left noetherian and left artinian. It is shown that left noetherian l-rings are local left principal ideal rings. When R is a finite dimensional algebra over a field, the property of being an l-ring is equivalent to being an r-ring. However, examples are given to show that these two concepts are in general not equivalent even in the artinian case.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1979 , pp. 51 - 58
Copyright
Copyright © Australian Mathematical Society 1979

References

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