Vol. 53, No. 2, 1974

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Direct sum subset decompositions of Z

Carl E. Swenson

Vol. 53 (1974), No. 2, 629–633
Abstract

Let Z be the set of integers. In this paper it is shown that there is no effective characterization of all direct sum subset decompositions of Z i.e., where A + B = Z and the sums are distinct. Further the result is generalized to include decompositions of a product of sets where Z is a set in the product, and to cases where the number of subsets in the decomposition is greater than two.

Mathematical Subject Classification 2000
Primary: 10L05
Secondary: 05B10
Milestones
Received: 8 March 1973
Published: 1 August 1974
Authors
Carl E. Swenson