Weak -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

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Abstract: A ring *R* is called a (right) *wq*-ring if every right ideal not isomorphic to 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 for some division ring *D*, or *R* is such that every right ideal not isomorphic to is completely reducible.

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Additional Information

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