Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 587922
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] E. P. Armendariz and J. W. Fisher, Idealizers in rings, J. Algebra 39 (1976), 551-562. MR 0396683 (53:545)
  • [2] J. S. Golan, Localization of noncommutative rings, Marcel Dekker, New York, 1975. MR 0366961 (51:3207)
  • [3] K. R. Goodearl, Idealizers and nonsingular rings, Pacific J. Math. 48 (1973), 395-402. MR 0389979 (52:10808)
  • [4] B. Stenstrom, Rings of quotients, Springer-Verlag, New York, 1975. MR 0389953 (52:10782)
  • [5] M. L. Teply, Prime singular splitting rings with finiteness conditions, Lecture Notes in Math., vol. 545, Springer-Verlag, Berlin, 1976. MR 0435141 (55:8102)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A63, 16A08

Retrieve articles in all journals with MSC: 16A63, 16A08

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society