Toma Albu, Jaime Castro Pérez, José Ríos Montes: The lattice structure of all lattice preradicals on modular complete lattices, and applications (I), 3-20

Abstract:

Based on the concept of a linear morphism of lattices, recently introduced in the literature, we present and investigate in this paper the latticial counterpart of the big lattice R-pr of all preradicals on the category Mod-R of all unital right R-modules over an associative ring R with identity.

Key Words: modular lattice, upper continuous lattice, linear morphism of lattices, fully invariant submodule, fully invariant element, lattice preradical, big lattice, Grothendieck category, hereditary torsion theory.

2010 Mathematics Subject Classification: Primary 06C05. Secondary 06C99, 06B35, 16D80, 16S90, 18E15.