The Maximal A-regular Submodule of Module

Abstract

Let R be commutative ring with identity and all module are (left) unitary R-module. An R-module M is saidi to be almost regular (for short A-regular) module if every submodule is almost pure (for short A-pure) submodule of M. In thisi paper we show that each unitary R-module has unique maximal A-regular submodule which is denoted by L(M), means a submodule of M which contains every A-regular submodule of M. Wei proved that if M is an R-module and N is a submodule of M, then L(N) = N ∩ L(M).