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- Title
# Semi M-Projective and Semi N-Injective Modules.

- Authors
## HAKMI, HAMZA

- Abstract
## Let M and N be modules over a ring R. The purpose of this paper is to study modules M,N for which the bi-module [M,N] is regular or pi. It is proved that the bi-module [M,N] is regular if and only if a module N is semi M-projective and Im(α) ⊆⊗ N for all α 2 [M,N], if and only if a module M is semi N-injective and Ker(α) ⊆⊗ N for all α ϵ [M,N]. Also, it is proved that the bi-module [M,N] is pi if and only if a mod- ule N is direct M-projective and for any α ϵ [M,N] there exists β ϵ [N,M] such that Im(αβ) ⊆⊗ N, if and only if a module M is direct N-injective and for any α ϵ [M,N] there exists β ϵ [N,M] such that Ker(βα) ⊆⊗ M. The relationship between the Jacobson radical and the (co)singular ideal of [M,N] is described.

- Subjects
## INJECTIVE modules (Algebra); PROJECTIVE geometry; MATHEMATICAL functions; MODULES (Algebra); SINGULAR integrals

- Publication
## Kyungpook Mathematical Journal, 2016, Vol 56, Issue 1, p83

- ISSN
## 1225-6951

- Publication type
## Academic Journal

- DOI
## 10.5666/KMJ.2016.56.1.83