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Commutative rings whose factors have Artinian rings of quotients

Published online by Cambridge University Press:  17 April 2009

William D. Blair
William D. Blair
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115, USA.
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Abstract

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Let R be a commutative ring with unity. Then every factor ring of R has an Artinian total quotient ring if and only if R is a direct sum of one-dimensional Noetherian domains and local Artinian rings.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 9 - 12
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Camillo, Victor P., “Commutative rings whose quotients are Goldie”, Glasgow Math. J. 16 (1975), 32–33.Google Scholar
[2]Cohen, I.S., “Commutative rings with restricted minimum condition”, Duke Math. J. 17 (1950), 27–42.CrossRefGoogle Scholar
[3]Small, Lance W., “Orders in Artinian rings”, J. Algebra 4 (1966), 13–41.CrossRefGoogle Scholar