# commutative

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## commutative

Maths Logic
a. (of an operator) giving the same result irrespective of the order of the arguments; thus disjunction and addition are commutative but implication and subtraction are not
b. relating to this property
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
For any commutative semiring, one has f(A) [less than or equal to] t(A) whenever A is an m byn matrix over S.
Theorem 4.1 Let B be a finite left regular band, k a commutative ring with unit, and X,Y G A (B).
Beck, "Coloring of commutative rings," Journal of Algebra, vol.
In constructing the course outline, faculty listed the following topics as possible topics for a first course in commutative algebra and algebraic geometry.
This proves that the diagram is commutative. Also, the corresponding relations are presented as
His movements may be guided principally by commutative justice, which usually poses no knowledge problem at all.
They learned that a perfect square does not have a commutative partner.
Since R is a commutative unitalring, [([r.sup.2] + r).sup.2] = [r.sup.2] x [(r + 1).sup.t] = [r.sup.t] x [b.sup.t].
Every unital (commutative or not) normed algebra (similarly, every unital p-normed algebra with p [member of] (0,1]) is a TQ-algebra, hence also a TQ-algebras (see , Proposition 2.6).
For commutative semirings, needless to say, the notions of left and right Euclidean norm coincide.
In (11), Herstein proved that if R is a prime ring with char R [not equal to] 2 and R admits a non-zero derivation d such that [d(x), d(y)] = 0 for all x, y [member of] R, then R is commutative. In (10), Filippis showed that if R be a prime ring of characteristic dierent from 2, d a non-zero derivation of R and [rho] a non-zero right ideal of R such that [[rho], [rho]][rho] [not equal to] 0 and [[d(x), x], [d(y), y]] = 0 for all x, y [member of] [rho], then d([rho])[rho] = 0.
Let N be a weak commutative near-ring without non-zero zero divisors.

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