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Uniqueness of complementing pairs in partially ordered abelian groups

Published online by Cambridge University Press:  09 April 2009

Rodney T. Hansen
Rodney T. Hansen
Affiliation:
Montana State University
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Let A and B denote subsets of an abelian group (G, +). The pair (A, B) is called a complementing pair for A + B provided each element of the sum is uniquely represented. A complementing pair (A, B) for C is denoted (A, B) ~ C.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 15 - 16
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]McLeod, R. M. and Spira, R., ‘Direct sum decomposition of the non-negative integers’, Unpublished, (1966).Google Scholar
[2]Hansen, R. T., ‘Complementing Pairs of Subsets of the Plane’, Duke Math. J. 36 (1969), 441–449.CrossRefGoogle Scholar