On absolutely torsion-free rings

Jorge Viola-Prioli

Vol. 56 (1975), No. 1, 275–283

DOI: 10.2140/pjm.1975.56.275

Abstract

Let K(R) denote the set of the kernel functors of the ring R and let ∞ be the trivial kernel functor defined by setting ∞(M) = M for every right module M. The absolutely torsion-free rings, that is, the rings R for which σ(R) = 0 for all σ ∈ K(R),σ≠∞, have been introduced by Rubin as a non commutative analogue of the integral domains.

In this paper a categorical characterization (in terms of finitely generated projective modules) of absolutely torsion-free rings is obtained. As a consequence, all of Rubin’s results are proved in a different fashion and generalization of most of them are provided. Additional properties of this class of rings are also exhibited.

Finally, absolutely torsion-free rings with torsionless injective hull are also considered.

Mathematical Subject Classification

Primary: 16A12

Milestones

Received: 25 October 1973

Revised: 3 September 1974

Published: 1 January 1975