When is the maximal ring of quotients projective?

Author:
David Handelman

Journal:
Proc. Amer. Math. Soc. **52** (1975), 125-130

MSC:
Primary 16A08

DOI:
https://doi.org/10.1090/S0002-9939-1975-0389955-7

MathSciNet review:
0389955

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Abstract: Let be an associative ring with , and its maximal ring of right quotients. If belongs to , a right insulator for in is a finite subset of , such that the right annihilator of is zero. Then we have: If is a projective right -module, is finitely generated; if is nonsingular, then is projective as a right -module if and only if there exists in such that is injective and has a right insulator in ; under these circumstances, if and only if has a left insulator in . We prove some related results for torsionless , and give an example of a prime ring such that is a cyclic projective right -module, but .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0389955-7

Keywords:
Ring of quotients,
projective,
injective,
torsionless,
nonsingular,
prime ring,
regular ring,
simple ring

Article copyright:
© Copyright 1975
American Mathematical Society