Some aspects of torsion

James Patrick Jans

Vol. 15 (1965), No. 4, 1249–1259

DOI: 10.2140/pjm.1965.15.1249

Abstract

Using S. E. Dickson’s characterization of a torsion class, a class of modules closed under taking factors extensions and arbitrary direct sum, we study torsion classes closed under taking submodules and arbitrary direct products. We show that these classes are in one-to-one correspondence with idempotent two sided ideals of the ring. Finally we investigate the structure of rings R for which the torsion class 𝒯₀ = {M|Hom_R(M,Q(R)) = 0, Q(R) the minimal injective for R} is closed under taking products.

Mathematical Subject Classification

Primary: 18.15

Secondary: 18.20

Milestones

Received: 15 July 1964

Published: 1 December 1965