Vol. 98, No. 2, 1982

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ISSN: 0030-8730
Rings on certain mixed abelian groups

David R. Jackett

Vol. 98 (1982), No. 2, 365–373
Abstract

This paper is concerned with the ring structures supported by certain mixed abelian groups. A class of mixed abelian groups of torsion-free rank one is introduced, and properties of rings on groups in are discussed. We provide complete descriptions of the absolute annihilator and the absolute radical of groups in . These absolute ideals are also investigated for cotorsion groups and reduced algebraically compact groups, thus providing a partial solution to Problem 94 of Fuchs (Infinite abelian groups, Vol. II). The results also allow us to answer a question raised by Rotman (J. Algebra, 9 (1968), 369–387) concerning completions of rings.

Mathematical Subject Classification 2000
Primary: 20K99
Milestones
Received: 25 February 1980
Revised: 15 December 1980
Published: 1 February 1982
Authors
David R. Jackett