Translation for 'polynomial ring' from English to Russian

polynomial ring

кольцо {с} многочленовмат.

---

Chebyshev polynomial

многочлен {м} Чебышёвамат.

Advertisement

circus ring

цирковая арена {ж}

Einstein ring

кольцо {с} Эйнштейнаастрон.физ.

local ring

локальное кольцо {с}мат.

ring galaxy

кольцеобразная галактика {ж}астрон.

(boxing) ring

(боксёрский) ринг {м}спорт

ring buoy

спасательный круг {м}морс.

life ring

спасательный круг {м}морс.

ring finger

безымянный палец {м}

ring [circle]

круг {м}

ring theory

теория {ж} колецмат.

ring [ornament, circle]

кольцо {с}

ring-billed gull

делавэрская чайка {ж} [Larus delawarensis]орн.T

to ring (up) sb. [telephone]

unverified звонить кому-л. по телефонутелеком.

to ring (up) [Br.] [to phone]

звонить [несов.]

algebra over a ring

unverified алгебра {ж} над кольцоммат.

ring [with stone or signet ring]

перстень {м}

• It turns out that an algebraic set is a variety if and only if it may be defined as the vanishing set of a prime ideal of the polynomial ring.
• In mathematics, specifically commutative algebra, Hilbert's basis theorem says that a polynomial ring over a Noetherian ring is Noetherian.
• The Krull dimension was introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety defined by an ideal "I" in a polynomial ring "R" is the Krull dimension of "R"/"I".
• the polynomial ring over GF(2). Rather than integer addition and multiplication, the basic operations are exclusive-or and carry-less multiplication, which is usually implemented as a sequence of logical shifts.
• It is common to construct an extension field of a given field "K" as a quotient ring of the polynomial ring "K"[...] in order to "create" a root for a given polynomial "f"("X").

• abstractly as the completion of the polynomial ring [...] equipped with a particular metric.
• The monoid N"n" (with the addition) gives the polynomial ring with "n" variables: "R"[...] =: "R"..., "X'n".
• Let [...] , the polynomial ring over the finite field with "q" elements. "A" is a principal ideal domain and therefore "A" is a unique factorization domain.
• corresponds to the set of prime ideals of the polynomial ring [...] , and the type-definable sets are exactly the affine varieties.
• In mathematics, a field [...] is algebraically closed if every non-constant polynomial in [...] (the univariate polynomial ring with coefficients in [...]) has a root in [...].

• For example, when working in the polynomial ring of integers: the greatest common divisor of [...] and [...] is "x", but there does not exist any integer-coefficient polynomials "p" and "q" satisfying [...].
• The connection to representation theory is clearer if one considers the polynomial ring [...] or, without a basis, [...] As the latter formulation makes clear, a polynomial ring is the group algebra over a vector space, and writing in terms of [...] corresponds to choosing a basis for the vector space.