SUBLATTICES OF R-TORS INDUCED BY A-MODULES

Authors : Jaime Castro PÉREZ, Gerardo Aguilar SÁNCHEZ

Pages : 17-36

View : 23 | Download : 11

Publication Date : 2012-12-01

Article Type : Research Paper

Abstract :This article is concerned with the study of the sublattice gen insert ignore into journalissuearticles values(ρ); of R-tors, where ρ is some arbitrary but fixed member of R-tors. We use the concept of the ρ-A-module insert ignore into journalissuearticles values(M is a ρ-A-module, if M is ρ-torsion free and ρ ∨ξ insert ignore into journalissuearticles values({M}); is an atom in gen insert ignore into journalissuearticles values(ρ);); and we define an equivalence relation in the sublattice gen insert ignore into journalissuearticles values(ρ);. The partition associated to this equivalence relation allows us to get interesting information about this sublattice. As an application, we obtain new characterizations of ρ-artinian rings, ρ-semiartinian rings insert ignore into journalissuearticles values(a ring R is ρ-semiartinian if every non-zero ρ-torsion free R-module contains a τ- cocritical submodule); and rings with ρ-atomic dimension insert ignore into journalissuearticles values(rings such that for all σ ∈ gen insert ignore into journalissuearticles values(ρ); with σ 6= χ, there exists a σ-A-module);.
Keywords : torsion theories, lattices, A modules, atomic dimension, Gabriel dimension, left τ semiartinian rings, left τ artinian rings