Topologies on the torsion-theoretic spectrum of a noncommutative ring

Jonathan Samuel Golan

Vol. 51 (1974), No. 2, 439–450

DOI: 10.2140/pjm.1974.51.439

Abstract

Let R-sp be the collection of all prime torsion theories on the category of left R-modules over an associative ring R. Three topologies—the order topology, the finitary order topology, and the reverse order topology (in the case that R is left noetherian)—are defined on R-sp and each is shown to exhibit some properties of the Zariski topology on the spectrum of a commutative ring. A fourth topology—the Gillman topology—is defined on R-sp when R is left noetherian and is used to characterize the separation of the reverse order topology.

Mathematical Subject Classification

Primary: 16A64

Milestones

Received: 12 December 1972

Published: 1 April 1974