Bases for commutative semigroups and groups
2008 ◽
Vol 145
(3)
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pp. 579-586
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Keyword(s):
AbstractA 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.
Keyword(s):
1992 ◽
Vol 34
(2)
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pp. 133-141
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1990 ◽
Vol 108
(3)
◽
pp. 429-433
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2011 ◽
Vol 18
(spec01)
◽
pp. 881-888
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Keyword(s):
Keyword(s):
2021 ◽
Vol 12
(3)
◽
pp. 5150-5155