Vol. 15, No. 4, 1965

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ISSN: 0030-8730
Some aspects of torsion

James Patrick Jans

Vol. 15 (1965), No. 4, 1249–1259
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|HomR(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
Authors
James Patrick Jans