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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Goldie conditions in finite normalizing extensions


Author: Charles Lanski
Journal: Proc. Amer. Math. Soc. 79 (1980), 515-519
MSC: Primary 16A34; Secondary 16A26
MathSciNet review: 572292
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Abstract: Let S be a finite normalizing extension of a ring R. If M is an S module, then M has finite uniform dimension if and only if it has finite uniform dimension when considered as an R module. Consequently, when S is a right Goldie ring, R is also a right Goldie ring. Conversely, if R is a semiprime right Goldie ring and S is a prime ring, then S is a Goldie ring. Finally, when both S and R are semiprime right Goldie rings, the quotient ring of R embeds in the quotient ring of S.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572292-7
PII: S 0002-9939(1980)0572292-7
Article copyright: © Copyright 1980 American Mathematical Society