# commutative group

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## commutative group

n.
A mathematical group in which the result of multiplying one member by another is independent of the order of multiplication. Also called abelian group.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 commutative group - a group that satisfies the commutative lawAbelian groupmathematical group, group - a set that is closed, associative, has an identity element and every element has an inverse
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References in periodicals archive ?
Now that NTV is a commutative group with respect to "*", we have [parallel]x * anti (z) * k * anti (k} [parallel]= [parallel] (x * anti (k)) * (anti (z) * [parallel] [less than or equal to] max{[parallel]x * anti(k) [parallel], [parallel]k * anti (z):)) [parallel]} [less than or equal to] [parallel]x * anti(*)[parallel] + [parallel]k * anti(z)) [parallel].
Then M is a commutative group as shown in (15) (see [12]).
Let Hom(S[|.sub.U],S'[|.sub.U]) be a commutative group of sheaf morphisms S [|.sub.U] [right arrow] S'[|.sub.U] for any open subset U [subset] X.
Several elementary properties of the space A[P.sub.[phi]](R, C), about its algebraic and topological structures have been already mentioned above: algebraically it is an additive and commutative group of formal series and topologically (convergence) it is a metric space.
Coverage includes a guide to closure operations in commutative algebra, a survey of test ideals, finite-dimensional vector spaces with Frobenius action, finiteness and homological conditions in commutative group rings, regular pullbacks, noetherian rings without finite normalization, Krull dimension of polynomial and power series rings, the projective line over the integers, on zero divisor graphs, and a closer look at non-unique factorization via atomic decay and strong atoms.
Semirings (called also halfrings) are algebras (R, +, x) share the same properties as a ring except that (R, +) is assumed to be a semigroup rather than a commutative group. Semirings appear in a natural manner in some applications to the theory of automata and formal languages (see [1]).

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