Vol. 51, No. 2, 1974

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Topologies on the torsion-theoretic spectrum of a noncommutative ring

Jonathan Samuel Golan

Vol. 51 (1974), No. 2, 439–450

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
Received: 12 December 1972
Published: 1 April 1974
Jonathan Samuel Golan