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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DOI:
https://doi.org/10.1090/S0002-9939-1980-0572292-7

Article copyright:
© Copyright 1980
American Mathematical Society