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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Quotient rings of a ring and a subring which have a common right ideal


Author: Jay Shapiro
Journal: Proc. Amer. Math. Soc. 80 (1980), 537-543
MSC: Primary 16A63; Secondary 16A08
DOI: https://doi.org/10.1090/S0002-9939-1980-0587922-3
MathSciNet review: 587922
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Abstract: Let R be a subring of S and let $ A \subseteq R$ be a right ideal of S. In this paper we show that there is a bijection between right torsion theories $ \tau $ over S such that A is $ \tau $-dense and right torsion theories $ \sigma $ over R such that S/A is $ \sigma $-torsion. A similar result is obtained for the left side with the bijection between torsion theories over S with SA dense and torsion theories over R with RA dense. It is also shown that the ring of quotients of R and S at these corresponding torsion theories are equal. As a corollary, when A is chosen appropriately R and S have the same right (left) maximal quotient ring.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587922-3
Article copyright: © Copyright 1980 American Mathematical Society