IJPAM: Volume 19, No. 1 (2005)

ON REGULAR MODULE

N. Amiri$^1$, M. Ershad$^2$
$^{1,2}$Department of Mathematics
Shiraz University
Shiraz, 71454, IRAN
$^1$e-mail: amiri@susc.ac.ir
$^2$e-mail: ershad@hafez.shirazu.ac.ir


Abstract.In this paper we shall consider some properties of regular modules. We show that every submodule of a divisible regular module over an integral domain is divisible and we also show that $J(R)M=0$ for every regular $R$-module $M$. It is shown that if every simple $R$-module is regular then $% J(R)=\cap \text{\rm ann}\,(M)$, where the intersection is over all regular $R$-module. If $% J(R) \neq 0$ and $M$ is a finitely generated regular $R$-module, then every prime submodule of $M$ is maximal. In this paper, $R$ will be a commutative ring with identity and all modules are unitary.

Received: December 14, 2004

AMS Subject Classification: 13C13, 13C05

Key Words and Phrases: regular module, divisible regular module, simple $R$-module, commutative ring

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 1