Communications in Algebra

Rangaswamy, K.M.

doi: 10.1080/00927877408822022pmid: N/A

Gordon, Robert

doi: 10.1080/00927877408822023pmid: N/A

Handelman, D.

doi: 10.1080/00927877408822024pmid: N/A

Let R be a ring with 1, and Q its maximal ring of right quotients. We give a number of necessary and sufficient conditions on R so that q is prime regular. We obtain as corollaries conditions so that Q is a full linear ring or Q is simple and satisfies xy = 1 implies yx = 1.

Simis, Aron

doi: 10.1080/00927877408822025pmid: N/A

Carl, Faith

doi: 10.1080/00927877408822026pmid: N/A

For a ring R, the following two conditions are equivalent:. (1) If E is an indecomposable injective right R-module, then End ER is a field (not necesarily commutative). (2) Every co-irreducible rigtht ideal is critical. Since (2) has been characterized ideal-theoretically, this amounts to an ideal-theoretical characterization of (1). These rings come up to the study of (QI) rings in which every quasi-injective module is injective.