MAPPINGS BETWEEN MODULE LATTICES

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International Electronic Journal of Algebra
Volume:15 Issue:15
MAPPINGS BETWEEN MODULE LATTICES

MAPPINGS BETWEEN MODULE LATTICES

Pages : 173-195

View : 12 | Download : 9

Publication Date : 2014-06-01

Article Type : Research Paper

Abstract :We examine the properties of certain mappings between the lattice of ideals of a commutative ring R and the lattice of submodules of an R-module M, in particular considering when these mappings are lattice homomorphisms. We prove that the mapping λ from the lattice of ideals of R to the lattice of submodules of M defined by λinsert ignore into journalissuearticles values(B); = BM for every ideal B of R is a insert ignore into journalissuearticles values(lattice); isomorphism if and only if M is a finitely generated faithful multiplication module. Moreover, for certain but not all rings R, there is an isomorphism from the lattice of ideals of R to the lattice of submodules of an R-module M if and only if the mapping λ is an isomorphism.
Keywords : Lattice homomorphism, commutative ring, Prufer domain, multiplication module, Noetherian ring

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