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Bases for commutative semigroups and groups

Published online by Cambridge University Press:  01 November 2008

NEIL HINDMAN  and
DONA STRAUSS
NEIL HINDMAN
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20901, U.S.A. e-mail: nhindman@aol.com
DONA STRAUSS
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9J2. e-mail: d.strauss@hull.ac.uk
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Abstract

A base for a commutative semigroup (S, +) is an indexed set 〈xt〉t∈A in S such that each element x ∈ S is uniquely representable as Σt∈Fxt where F is a finite subset of A and, if S has an identity 0, then 0 = Σn∈Øxt. We investigate those commutative semigroups or groups which have a base. We obtain the surprising result that has a base. More generally, we show that an abelian group has a base if and only if it has no elements of odd finite order.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 145 , Issue 3 , November 2008 , pp. 579 - 586
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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