Difference between revisions of "Polynomial ring"
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== Description == | == Description == | ||
| − | 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. | + | Polynomial rings have influenced much of mathematics, from the [[Hilbert's basis theorem|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. | + | 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]]. | A closely related notion is that of the [[ring of polynomial functions]] on a [[vector space]]. | ||
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* [[Additive polynomial]] | * [[Additive polynomial]] | ||
* [[Commutative algebra]] | * [[Commutative algebra]] | ||
| + | * [[Hilbert's basis theorem]] | ||
* [[Laurent polynomial]] | * [[Laurent polynomial]] | ||
* [[Ring (mathematics]] | * [[Ring (mathematics]] | ||
Latest revision as of 09:10, 8 November 2016
In mathematics, especially in the field of abstract 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.
Description
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.
See also
- Additive polynomial
- Commutative algebra
- Hilbert's basis theorem
- Laurent polynomial
- Ring (mathematics
- Ring of polynomial functions
External links
- Polynomial ring @ Wikipedia
