Mutually essentially pseudo injective modules, to appear (2013)

Mutually essentially pseudo injective modules, to appear (2013)
Nơi đăng: The Bulletin of the Malaysian Mathematical Sciences Society, Số: , Trang: , Năm: 2014, Loại bài viết: Bài báo, Quốc gia: Quốc tế.

Tóm tắt:

Let $M$ and $N$ be two modules. $M$ is called essentially pseudo $N$-injective if for any essential submodule $A$ of $N$, any monomorphism $f : A \rightarrow M$ can be extended to some $g \in Hom(N, M)$. $M$ is called essentially pseudo injective if $M$ is essentially pseudo $M$-injective. Basic properties of mutually essentially pseudo injective modules and essentially pseudo injective modules are proved and their connections with pseudo-injective modules are addressed.

Abstract:

Let $M$ and $N$ be two modules. $M$ is called essentially pseudo $N$-injective if for any essential submodule $A$ of $N$, any monomorphism $f : A \rightarrow M$ can be extended to some $g \in Hom(N, M)$. $M$ is called essentially pseudo injective if $M$ is essentially pseudo $M$-injective. Basic properties of mutually essentially pseudo injective modules and essentially pseudo injective modules are proved and their connections with pseudo-injective modules are addressed.