Commutative Self-Injective Rings

Singh, Surjeet ; Wasan, Kamlesh

Canadian journal of mathematics, Tome 22 (1970) no. 6, pp. 1101-1108

Résumé

All rings considered here are commutative containing at least two elements, but may not have identity. A ring R is said to be selfinjective if R as an R-module is injective. A ring R is said to be pre-selfinjective if every proper homomorphic image of R is self-injective [9]. Study of pre-self-injective rings was initiated by Levy [10], who established a characterization of Noetherian pre-self-injective rings with identity in terms of other well-known types of rings. Recently Klatt and Levy [9] have characterized all pre-self-injective rings with identity. In this paper we are mainly interested in Noetherian rings. For the sake of convenience we shall call a pre-self-injective ring an (I)-ring. A ring R will be said to be a (PMI)-ring if for each proper prime ideal P with P 2 ≠ 0, the ring R/P 2 is self-injective. Clearly, an (I)-ring is a (PMI)-ring.

Détail

DOI : 10.4153/CJM-1970-127-8

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