What does polynomial ring mean?

Definitions for polynomial ring
po·ly·no·mial ring

This dictionary definitions page includes all the possible meanings, example usage and translations of the word polynomial ring.

Wikipedia

  1. Polynomial ring

    In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial ring" refers implicitly to the special case of a polynomial ring in one indeterminate over a field. The importance of such polynomial rings relies on the high number of properties that they have in common with the ring of the integers. Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings. A closely related notion is that of the ring of polynomial functions on a vector space, and, more generally, ring of regular functions on an algebraic variety.

Wikidata

  1. Polynomial ring

    In mathematics, especially in the field of abstract algebra, a polynomial ring is a ring formed from the set of polynomials in one or more variables with coefficients in another ring. Polynomial rings have influenced much of mathematics, from the Hilbert basis theorem, to the construction of splitting fields, and to the understanding of a linear operator. Many important conjectures involving polynomial rings, such as Serre's problem, have influenced the study of other rings, and have influenced even the definition of other rings, such as group rings and rings of formal power series. A closely related notion is that of the ring of polynomial functions on a vector space.

How to pronounce polynomial ring?

How to say polynomial ring in sign language?

Numerology

  1. Chaldean Numerology

    The numerical value of polynomial ring in Chaldean Numerology is: 6

  2. Pythagorean Numerology

    The numerical value of polynomial ring in Pythagorean Numerology is: 9


Translations for polynomial ring

From our Multilingual Translation Dictionary

  • बहुपद वलयHindi
  • polynomringNorwegian
  • பல்லுறுப்புக்கோவை வளையம்Tamil

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"polynomial ring." Definitions.net. STANDS4 LLC, 2024. Web. 18 Mar. 2024. <https://www.definitions.net/definition/polynomial+ring>.

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