Vol. 95, No. 1, 1981

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ISSN: 0030-8730
On rings with bounded annihilators

John Allen Beachy and William David Blair

Vol. 95 (1981), No. 1, 1–10
Abstract

Commutative rings for which the annihilator of each finitely generated module is determined by n or fewer elements are studied. For Artinian rings the bound n is explicitly determined. Noetherian rings satisfying this condition are of Krull dimension one. A new characterization of Dedekind domains is given, and the relationship between the bound and the number of generators of ideals is studied.

Mathematical Subject Classification 2000
Primary: 13F05
Secondary: 16A34
Milestones
Received: 18 April 1980
Published: 1 July 1981
Authors
John Allen Beachy
William David Blair