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In this presentation we give a surjective order preserving function between the lattice of Natural Classes and the lattice of Hereditary Torsion Theories. Also we show that this function is a lattice morphism precisely when it is a lattice isomorphism and this happens if and only if the ring R is a left semiartinian ring.

References:

1. Alejandro Alvarado-Garca , Csar Cejudo-Castilla , Hugo Alberto Rincn-Meja & Ivan Fernando Vilchis- Montalvo, Rings for Which the Lattice of Hereditary Torsion Theories and the Lattice of Natural Classes are Isomorphic, Communications in Algebra 41:11 (2013) 4089-4097