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.