**ROGER YUE CHI MING**

*On injectivity and p-injectivity, III*

**Pages:** 45-50

**Received:** 6 May 2000
**Revised:** 15 March 2001

**Mathematics Subject Classification (2000):** 16A30 - 16A34 - 16A36

**Abstract**:
In this sequel to [18], [19], it is shown that the
following conditions are equivalent for a commutative ring A : (1) Every
factor ring of A is quasi - Frobeniusean ; (2) Every factor ring of A is a
p - injective ring with maximum condition on annihilators.
Also, the following conditions are equivalent for any ring A : (1) Every
factor ring of A is left self - injective regular with non - zero socle
; (2) Every factor ring of A is a semi - prime ring with an injective
maximal left ideal. A right Noetherian ring whose factor rings are left p
- injective must be right Artinian.

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