Quasi-pseudo Principally Injective Modules

Abstract

In this paper, the concept of quasi-pseudo principally injective modules is introduced and a characterization of commutative semi-simple rings is given in terms of quasi-pseudo principally injective modules. An example of pseudo M -p-injective module which is not M -pseudo injective is given.

Some aspects of quasi-pseudo principally injective modules

“…Using this results we can conclude that if R R is self-similar and semi-simple, then the ring R is self-pseudo principally injective (self-pseudo-p-injective). Proposition 2.6 [4]. Every quasi-pp-injective module satisfies C 2 .…”

Generalization of Semi-Projective Modules

“…Motivated by this definition, authors have introduce the notion of quasi-pseudo principally projective module in [10] which is the dual notion of quasi-pseudo principally injective module defined by Chaturvedi et.al. [2]. In [11] T.C.Quynh have studied the same under the name Pseudo semi-projective Modules, Now authors are in position to prove the various property of such modules.…”