On quasi-injective modules with a chain condition over a commutative ring

Manabu Harada
1972
In the previous paper [4] the author and T. Ishii studied the endomorphism rings of noetherian quasi-injective modules. As an application of it, we consider, in this paper, quasi-injective modules over a commutative ring R. If i? is noetherian, E. Matlis decided every indecomposable injective modules in [6] . Greatly making use of those results in [6], we shall decide all quasi-injective (resp. injective) modules which are either artinian or noetherian in § §2 and 3. Especially, we shall give
more » ... ly, we shall give necessary and sufficient conditions of R for existence of quasi-injective (resp. injective) modules which are either artinian or noetherian (cf. [7], Theorem 5). In this paper, a ring R is always commutative unless otherwise stated and every i?-module is unitary.
doi:10.18910/12866 fatcat:k7yb4hyfy5dw7dwi7iopvc3wfy