MAPPINGS BETWEEN MODULE LATTICES
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 λ(B) = BM for every ideal B of R is a (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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- Department of Mathematics University of Glasgow Glasgow G12 8QW, Scotland UK e-mail: Patrick.Smith@glasgow.ac.uk
- ISSN: 1306-6048
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2007
- Yayıncı: Abdullah HARMANCI
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