Bases for commutative semigroups and groups
نویسنده
چکیده
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 ∑t∈F xt where F is a finite subset of A and, if S has an identity 0, then 0 = ∑n∈ xt . We investigate those commutative semigroups or groups which have a base. We obtain the surprising result that Q 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.
منابع مشابه
Subject Classiication (ams)
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تاریخ انتشار 2008