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Polynomial ring
| Algebraic structure → Ring theory Ring theory |
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Rings
Related structures
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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.[1]
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.[2]
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.[3]
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.[2]
- ^ "Index", The Art of Legal Problem Solving, Cambridge University Press, pp. 123–126, 2024-03-11, doi:10.1017/9781009457927.012, ISBN 978-1-009-45792-7, retrieved 2024-09-14
- ^ a b "polynomial ring". planetmath.org. Retrieved 2024-09-14.
- ^ "Art of Problem Solving". artofproblemsolving.com. Retrieved 2024-09-14.
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