Definition, Betydelse & Synonymer | Engelska ordet COMMUTATIVE

Definition av COMMUTATIVE

1. (matematik) kommutativ

Exempel på hur du använder COMMUTATIVE i en mening

• Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.
• His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
• In mathematics, an associative algebra A over a commutative ring (often a field) K is a ring A together with a ring homomorphism from K into the center of A.
• In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
• In mathematics, the ascending chain condition (ACC) and descending chain condition (DCC) are finiteness properties satisfied by some algebraic structures, most importantly ideals in certain commutative rings.
• In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.
• Hilbert discovered and developed a broad range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).
• Wedderburn's little theorem asserts that all finite division rings are commutative and therefore finite fields.
• In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
• A natural example of a preorder is the divides relation "x divides y" between integers, polynomials, or elements of a commutative ring.
• The order in which real or complex numbers are multiplied has no bearing on the product; this is known as the commutative law of multiplication.
• In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a commutative ring without nonzero zero divisors) in which every ideal is principal (that is, is formed by the multiples of a single element).
• If A is such an algebraic set, one considers the commutative ring R of all polynomial functions A → K.
• The dual numbers form a commutative algebra of dimension two over the reals, and also an Artinian local ring.
• A subalgebra of an algebra over a commutative ring or field is a vector subspace which is closed under the multiplication of vectors.
• Maximal ideals are important because the quotients of rings by maximal ideals are simple rings, and in the special case of unital commutative rings they are also fields.
• In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist.
• Since the Gaussian integers are closed under addition and multiplication, they form a commutative ring, which is a subring of the field of complex numbers.
• Every cyclic group is an abelian group (meaning that its group operation is commutative), and every finitely generated abelian group is a direct product of cyclic groups.
• In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals.

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