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Polynomial ring

In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.

Products, Univariate polynomials over a field & Definition (multivariate case)

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Overview

Definition (univariate case)

Univariate polynomials over a field

Definition (multivariate case)

Graded structure

Univariate over a ring vs. multivariate

Several indeterminates over a field

Generalizations

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Map overview Semantic statistics

Polynomial ring

Nodes193
Edges192
Triples73
Avg. degree1.99
Density0.010363
Components1

How this topic connects Entity context

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Polynomial ring

Top relations

related to References · 22
Polynomial ring → Abstract Algebra, Algebra, An Introduction, Basic, Cambridge University Press, First Course, Graduate Texts, Hall, ISBN, Lam, Mathematics, MR, New York, Noncommutative Rings, Revised, Scott, Section, Serge, Springer-Verlag, Topics
related to Several indeterminates over a field · 7
Polynomial ring → Bézout's, Hilbert's Nullstellensatz, In, Jacobian, Polynomial, Some, This
related to Categorical characterization · 6
Polynomial ring → As, If, K-algebra, This, X1, Xn
related to Infinitely many variables · 6
Polynomial ring → Each, However, One, Such, This, Thus
related to Power series · 6
Polynomial ring → Alternatively, Cauchy, For, Power, The, This
related to Noncommutative polynomial rings · 5
Polynomial ring → For, Formally, Just, Neither, R-algebra
related to Differential and skew-polynomial rings · 4
Polynomial ring → It, Other, The, This
related to Definition (univariate case) · 3
Polynomial ring → Let, One, The
related to Formal partial derivatives · 3
Polynomial ring → Given, Hence, Similarly
is a · 2
Polynomial ring → graded ring, ring of differential operators formed from a ring R and a derivation δ of R into R

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Important terminology

polynomial ring displaystyle polynomials field one coefficients degree rings case algebra set ldots zero two unique commutative indeterminates defined product

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Polynomial ringis agraded ring0.90text
Polynomial ringis aring of differential operators formed from a ring R and a derivation δ of R into R0.90text
number theoryinstance ofThe 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 funda…0.80text
commutative algebrainstance ofThe 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 funda…0.80text
and algebraic geometryinstance ofThe 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 funda…0.80text
Polynomial ringrelated to Categorical characterizationIf0.60section
Polynomial ringrelated to Categorical characterizationX10.60section
Polynomial ringrelated to Categorical characterizationXn0.60section
Polynomial ringrelated to Categorical characterizationK-algebra0.60section
Polynomial ringrelated to Categorical characterizationThis0.60section
Polynomial ringrelated to Categorical characterizationAs0.60section
Polynomial ringrelated to Definition (univariate case)Let0.60section

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