Direct Sums of Injective and Projective Modules
نویسندگان
چکیده
It is well-known that a countably injective module is Σ-injective. In Proc. Amer. Math. Soc. 316, 10 (2008), 3461-3466, Beidar, Jain and Srivastava extended it and showed that an injective module M is Σ-injective if and only if each essential extension of M(א0) is a direct sum of injective modules. This paper extends and simplifies this result further and shows that an injective module M is Σ-injective if and onIy if each essential extension of M(א0) is a direct sum of modules that are either injective or projective. Some consequences and generalizations are also obtained.
منابع مشابه
ON PROJECTIVE L- MODULES
The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...
متن کاملOn weakly projective and weakly injective modules
The purpose of this paper is to further the study of weakly injective and weakly projective modules as a generalization of injective and projective modules. For a locally q.f.d. module M , there exists a module K ∈ σ[M ] such that K ⊕N is weakly injective in σ[M ], for any N ∈ σ[M ]. Similarly, if M is projective and right perfect in σ[M ], then there exists a module K ∈ σ[M ] such that K ⊕ N i...
متن کاملOn H-cofinitely supplemented modules
A module $M$ is called $emph{H}$-cofinitely supplemented if for every cofinite submodule $E$ (i.e. $M/E$ is finitely generated) of $M$ there exists a direct summand $D$ of $M$ such that $M = E + X$ holds if and only if $M = D + X$, for every submodule $X$ of $M$. In this paper we study factors, direct summands and direct sums of $emph{H}$-cofinitely supplemented modules. Let $M$ be an $emph{H}...
متن کاملOn character projectivity Of Banach modules
Let $A$ be a Banach algebra, $\Omega(A)$ be the character space of $A$ and $\alpha\in\Omega(A)$. In this paper, we examine the characteristics of $\alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.
متن کاملOn injective L-modules
The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove t...
متن کامل