Some aspects about the lattice [¿g,¿] and the torsion theories of Kaplansky-type Academic Article in Scopus uri icon

abstract

  • In this manuscript, we define when a torsion theory, which is a generalization of Goldie¿s torsion theory, is of the type I, II, or III, according to Kaplansky¿s theory of types, and we establish some structure theorems of regular, right self-injective rings using the torsion theories of Kaplansky-type. We study the properties that each of these torsion theories has and their influence on the lattice (Formula presented.) of generalizations of Goldie¿s torsion theory, locating several subintervals of (Formula presented.) which contain no atoms nor coatoms, thus extending our knowledge of the lattice structure of (Formula presented.). © 2023 Taylor & Francis Group, LLC.

publication date

  • January 1, 2023