Bases for commutative semigroups and groups

• Autores: Neil Hindman, Donna Strauss
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 3, 2008, págs. 579-586
• Idioma: inglés
• DOI: 10.1017/s0305004108001539
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• Resumen

  • A base for a commutative semigroup (S, +) is an indexed set xttA in S such that each element x S is uniquely representable as StF xt where F is a finite subset of A and, if S has an identity 0, then 0 = SnØxt. 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.