Weak 𝑞-rings with zero singular ideal

Mohamed, Saad; Singh, Surjeet

doi:10.1090/S0002-9939-1979-0534383-8

Weak $q$-rings with zero singular ideal
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by Saad Mohamed and Surjeet Singh PDF

Proc. Amer. Math. Soc. 76 (1979), 25-30 Request permission

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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