Vol. 64, No. 2, 1976

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Power-cancellation of groups and modules

Kenneth R. Goodearl

Vol. 64 (1976), No. 2, 387–411

This paper is concerned with deriving conditions which ensure that even though a module A may not necessarily cancel from a direct sum ABAC, it can at least be concluded that BnCn for some positive integer n. This conclusion is obtained from a type of stable range condition on the endomorphism ring of A, which holds, for example, when A is a finitely generated module over any subring of a finite-dimensional Q-algebra. As an application of these methods to groups, it is shown that if A is a torsion-free abelian group of finite rank, and B, C are arbitrary groups (not necessarily abelian) such that A × BA × C, then there exists a positive integer n such that the direct product of n copies of B is isomorphic to the direct product of n copies of C.

Mathematical Subject Classification
Primary: 16A64, 16A64
Received: 14 November 1975
Revised: 26 January 1976
Published: 1 June 1976
Kenneth R. Goodearl
University of California, Santa Barbara
Santa Barbara CA
United States