Resumen de Bases for commutative semigroups and groups

Neil Hindman, Donna Strauss

• 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.