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

Abstract

In this article we give a surjective order preserving function ϕ(): R-nat → R-tors which also preserves infima. We prove that ϕ(): 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(): R-nat → R-tors.

Key Words:

• Natural class
• R-tors
• Semiartinian ring

2010 Mathematics Subject Classification:

• 16D80

ACKNOWLEDGMENT

The authors wish to express their gratitude to the referee for his valuable remarks and suggestions.

Notes

Communicated by T. Albu.