skew polynomial ring wikipedia - EAS
- Skew polynomial rings.are considered with a multiplication defined by x • a = a 1 x + a 1 x 2 + … + a r x r, a i ∈ K, where K is a (skew) field and the ai depend on a ∈ K. Under certain conditions the rings appear to be non-commutative principal ideal rings with a unique factorization.Author: T.H.M. SmitsPublish Year: 1968
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See all on Wikipediahttps://en.wikipedia.org/wiki/Polynomial_ringIn 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,
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See moreThe polynomial ring, K[X], in X over a field (or, more generally, a commutative ring) K can be defined in several equivalent ways. One of them is to define K[X] as the set of expressions, called polynomials in X, of the form
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See moreGiven n symbols called indeterminates, a monomial (also called power product)
is a formal product of these indeterminates, possibly raised to a nonnegative power. As...
See morePolynomial rings in several variables over a field are fundamental in invariant theory and algebraic geometry. Some of their properties, such as those described above can be reduced to the case of a single indeterminate, but this is not always the case. In particular,
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See moreIf K is a field, the polynomial ring K[X] has many properties that are similar to those of the ring of integers Most of these similarities result from the similarity between the long division of integers and the long division of polynomials.
Most of the properties of...
See moreA polynomial in can be considered as a univariate polynomial in the indeterminate over the ring by regrouping the terms that contain the same power of that
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See morePolynomial rings can be generalized in a great many ways, including polynomial rings with generalized exponents, power series rings,
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See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Skew_polynomial_ring
In mathematics, especially in the area of algebra known as ring theory, an Ore extension, named after Øystein Ore, is a special type of a ring extension whose properties are relatively well understood. Elements of a Ore extension are called Ore polynomials.
Ore extensions appear in several natural contexts, including skew and differential polynomial rings, group algebras of polycyclic groups, universal enveloping algebras of solvable Lie algebras, and co…Wikipedia · Text under CC-BY-SA license - https://www.sciencedirect.com/science/article/pii/S1385725868500222
Skew polynomial rings .are considered with a multiplication defined by x • a = a 1 x + a 1 x 2 + … + a r x r, a i ∈ K, where K is a (skew) field and the ai depend on a ∈ K. Under certain conditions the rings appear to be non-commutative principal ideal rings with a unique factorization.
- Author: T.H.M. Smits
- Publish Year: 1968
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Polynomial ring - Wikipedia
https://static.hlt.bme.hu/.../en.wikipedia.org/wiki/Polynomial_ring.htmlIn 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.. Polynomial rings occur in many parts of mathematics, and the study of their properties was …
- https://en.wikipedia.org/wiki/Schur_polynomial
In mathematics, Schur polynomials, named after Issai Schur, are certain symmetric polynomials in n variables, indexed by partitions, that generalize the elementary symmetric polynomials and the complete homogeneous symmetric polynomials. In representation theory they are the characters of polynomial irreducible representations of the general linear groups. The Schur …
- https://en.wikipedia.org/wiki/Ideal_(ring_theory)
The set of all polynomials with real coefficients which are divisible by the polynomial x 2 + 1 is an ideal in the ring of all polynomials. The set of all n-by-n matrices whose last row is zero forms a right ideal in the ring of all n-by-n matrices. It is not a left ideal. ... The matrix ring over a skew-field is a simple ring.
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Nov 11, 2010 · Summary. We continue the study of skew polynomial rings in this chapter, first discussing the case where the multiplication is twisted by a derivation, and then developing the general case. Since our main motivation for looking at skew polynomial rings is to be able to construct and work with further important examples of noetherian rings, most ...
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Jan 22, 2022 ·
· However, A can be considered as a skew polynomial ring with respect to Y. The multiplication is modified, in view of the equality Y d = (X + c)d = α(d)X + cd = α(d)(X + c) + (cd − α(d)c), by an inner α-derivation δ c (d) = cd − α(d)c. Hence, A is now the skew polynomial ring D[Y, α, δ c].Up to
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In mathematics. Skew lines, neither parallel nor intersecting. Skew normal distribution, a probability distribution. Skew field or division ring. Skew-Hermitian matrix. Skew lattice. Skew polygon, whose vertices do not lie on a plane. Infinite skew polyhedron. Skew-symmetric graph.
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