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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
DOI: https://doi.org/10.1090/S0002-9939-1979-0534383-8
MathSciNet review: 534383
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0534383-8
Keywords: Quasi-injective module, singular submodule, dimension of a module, hereditary ring, q-ring
Article copyright: © Copyright 1979 American Mathematical Society