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)



Weak $ q$-rings with zero singular ideal

Authors: Saad Mohamed and Surjeet Singh
Journal: Proc. Amer. Math. Soc. 76 (1979), 25-30
MSC: Primary 16A48
MathSciNet review: 534383
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A ring R is called a (right) wq-ring if every right ideal not isomorphic to $ {R_R}$ is quasi-injective. The main result proved is the following: Let R be a ring with zero singular ideal, then R is a wq-ring if and only if either R is a q-ring, or $ R = \left[\begin{smallmatrix}0&D\\ D&D\end{smallmatrix}\right]$ for some division ring D, or R is such that every right ideal not isomorphic to $ {R_R}$ is completely reducible.

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

  • [1] K. A. Byrd, Right self-injective rings whose essential right ideals are two sided, Pacific J. Math. (to appear). MR 549830 (80m:16014)
  • [2] C. Faith, Algebra. II, Springer-Verlag, New York, 1975. MR 0427349 (55:383)
  • [3] M. Harada, Note on quasi-injective modules, Osaka Math. J. 2 (1965), 351-356. MR 0204464 (34:4306)
  • [4] G. Ivanov, Non-local rings whose ideals are all quasi-injective, Bull. Austral. Math. Soc. 6 (1972), 45-52. MR 0291217 (45:311)
  • [5] S. K. Jain, S. H. Mohamed and S. Singh, Rings in which every right ideal is quasi-injective, Pacific J. Math. 31 (1969), 73-79. MR 0251073 (40:4304)
  • [6] R. E. Johnson and E. T. Wong, Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260-268. MR 0131445 (24:A1295)
  • [7] Y. Miyashita, On quasi-injective modules, J. Fac. Sci. Hokkaido Univ. 18 (1965), 158-187. MR 0171817 (30:2044)
  • [8] S. Mohamed and S. Singh, Weak q-rings, Canad. J. Math. 29 (1977), 687-695. MR 0442026 (56:415)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 16A48

Retrieve articles in all journals with MSC: 16A48

Additional Information

Keywords: Quasi-injective module, singular submodule, dimension of a module, hereditary ring, q-ring
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society