Vol. 42, No. 1, 1972

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ISSN: 0030-8730
A duality for quotient divisible abelian groups of finite rank

David Marion Arnold

Vol. 42 (1972), No. 1, 11–15
Abstract

The usual duality for finite dimensional vector spaces induces a duality F on the category of torsion free quotient divisible abelian groups of finite rank with quasi-homomorphisms as morphisms. This duality preserves rank, is exact, hence preserves quasi-direct sums, sends free groups to divisible groups and conversely, and has the property that for all primes p, p-rank FA = rank A p-rank A.

Mathematical Subject Classification 2000
Primary: 20K15
Milestones
Received: 19 March 1971
Revised: 31 August 1971
Published: 1 July 1972
Authors
David Marion Arnold