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)

 
 

 

On quotient rings of trivial extensions


Author: Yoshimi Kitamura
Journal: Proc. Amer. Math. Soc. 88 (1983), 391-396
MSC: Primary 16A08; Secondary 16A65
DOI: https://doi.org/10.1090/S0002-9939-1983-0699400-4
MathSciNet review: 699400
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a ring with identity and $ M$ a two-sided $ R$-module. It is shown that every right quotient ring in the sense of Gabriel of the trivial extension of $ R$ by $ M$ is a trivial extension of a right quotient ring of $ R$ by a suitable two-sided module in case $ _RM$ is flat and finitely generated by elements which centralize with every element of $ R$.


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

  • [1] F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer-Verlag, Berlin and New York, 1974. MR 0417223 (54:5281)
  • [2] P. Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323-448. MR 0232821 (38:1144)
  • [3] V. K. Kharchenko, Galois extensions and quotient rings, Algebra i Logica 13 (1974), 460-484 (Russian); English transl., Algebra and Logic 13 (1974), 265-281 (1975). MR 0396636 (53:498)
  • [4] J. Lambek, On Utumi's rings of quotients, Canad. J. Math. 15 (1963), 363-370. MR 0147509 (26:5024)
  • [5] K. Morita, Localizations in categories of modules. I, Math. Z. 114 (1970), 121-144. MR 0263858 (41:8457)
  • [6] B. Müller, On Morita duality, Canad. J. Math. 21 (1969), 1338-1347. MR 0255597 (41:258)
  • [7] Y. Utumi, On quotient rings, Osaka Math. J. 8 (1956), 1-18. MR 0078966 (18:7c)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A08, 16A65

Retrieve articles in all journals with MSC: 16A08, 16A65


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0699400-4
Keywords: Trivial extension, quotient ring, injective module, biendomorphism ring
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society