IJPAM: Volume 19, No. 4 (2005)

ON REGULAR MODULES, II

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 study the relationship between the projectivity and regualarity. We shows that every projective module over a von Neumann regular ring is regular. We also show that a projective module $P$ is regular if and only if every cyclic submodule of $P$ is a direct summand of $P$ and we shall see that if $P$ is a projective regular module then $J(P)=Z(P)=0$, where $J(P)$ and $Z(P)$ are the Jacobson and singular submodules of $P$ respectively. $P$ is regular and indecomposible iff $P$ is projective and hollow. In this paper $R$ will be a commutative ring with identity and all modules are unitary.

Received: January 7, 2005

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: 4