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Bases for commutative semigroups and groups
Published online by Cambridge University Press: 01 November 2008
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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