IJPAM: Volume 56, No. 1 (2009)

ON $
\mathversion{bold} \mathscr{K}$-LIFTING MODULES

Fangdi Kong$^1$, Shuhui Peng$^2$
$^{1,2}$Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, 730050, P.R. CHINA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]

Abstract.Let $R$ be a ring and $M$ a left $R$-module. As a proper generalization of lifting module, we introduce the concept of $\mathscr{K}$-lifting module. $M$ is called a $\mathscr{K}$-lifting module if for every $f\in$End($M$), there exists a direct summand $K$ of $M$ such that $K\subseteq$Ker$f$ and Ker$f/K\ll M/K$. Some properties of $\mathscr{K}$-lifting modules are given.

Received: August 13, 2009

AMS Subject Classification: 16D99

Key Words and Phrases: $\mathscr{K}$-lifting module, fully invariant submodule

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1