Rings for Which the Lattice of Hereditary Torsion Theories and the Lattice of Natural Classes are Isomorphic

摘要

In this article we give a surjective order preserving function φ{symbol}: R-nat → R-tors which also preserves infima. We prove that φ{symbol}: R-nat → R-tors is a lattice morphism precisely when it is a lattice isomorphism and this happens if and only if R is a left semiartinian ring. We also study the fibers of φ{symbol}: R-nat → R-tors.