IJPAM: Volume 19, No. 1 (2005)
Department of Mathematics
Shiraz, 71454, IRAN
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 for every regular -module . It is shown that if every simple -module is regular then , where the intersection is over all regular -module. If and is a finitely generated regular -module, then every prime submodule of is maximal. In this paper, 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 -module, commutative ring
Source: International Journal of Pure and Applied Mathematics