MAPPINGS BETWEEN LATTICES OF RADICAL SUBMODULES

Authors : Hosein Fazaeli Moghimi, Javad Bagheri Harehdashti

Pages : 35-48

Doi:10.24330/ieja.266191

View : 17 | Download : 13

Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :Let R be a ring and Rinsert ignore into journalissuearticles values(M); be the lattice of radical submodules of an R-module M. Although the mapping ρ : Rinsert ignore into journalissuearticles values(R); → Rinsert ignore into journalissuearticles values(M); defined by ρinsert ignore into journalissuearticles values(I); = radinsert ignore into journalissuearticles values(IM); is a lattice homomorphism, the mapping σ : Rinsert ignore into journalissuearticles values(M); → Rinsert ignore into journalissuearticles values(R); defined by σinsert ignore into journalissuearticles values(N); = insert ignore into journalissuearticles values(N : M); is not necessarily so. In this paper, we examine the properties of σ, in particular considering when it is a homomorphism. We prove that a finitely generated R-module M is a multiplication module if and only if σ is a homomorphism. In particular, a finitely generated module M over a domain R is a faithful multiplication module if and only if σ is an isomorphism.
Keywords : σ modules, multiplication modules, primeful modules