Examples of 'polynomial ring' in a sentence
Meaning of "polynomial ring"
polynomial ring: In mathematics, a polynomial ring is a mathematical structure where polynomials in one or more variables can be added, subtracted, and multiplied following specific rules
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- A ring (which is also a commutative algebra), denoted K[X], formed from the set of polynomials (usually of one variable, in a given set, X), with coefficients in a given ring (often a field), K.
How to use "polynomial ring" in a sentence
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polynomial ring
Polynomial ring of one and more variables.
Quotient of polynomial ring.
Classical cyclic codes have a natural structure of ideals in a polynomial ring.
Matrices over a polynomial ring are important in the study of control theory.
The ring of power series can be seen as the completion of the polynomial ring.
Multivariate polynomial ring.
A polynomial ring over a Mori domain need not be a Mori domain.
It states that every finitely generated projective module over a polynomial ring is free.
If k is a field, then the polynomial ring k is an integral domain.
The theorem states that every finitely generated projective module over a polynomial ring is free.
Let R be the multivariate polynomial ring k over a field k.
It relies on the difficulty of factoring in a non-commutative polynomial ring.
Suppose that a ring R is a quotient of a polynomial ring k over a field by some ideal.
Borel 's theorem, which says the cohomology ring of a classifying stack is a polynomial ring.
Every field and every polynomial ring over a field ( in arbitrarily many variables ) is a reduced ring.
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More generally, the Chevalley-Shephard-Todd theorem characterizes finite groups whose algebra of invariants is a polynomial ring.
Weighted projective spaces can be constructed using a polynomial ring whose variables have non-standard degrees.
One example implementation includes a structural representation of a ring R, such as a polynomial ring.
Let C be the polynomial ring over the integers, in all these indeterminate coefficients.
The SWIFFT functions can be described as a simple algebraic expression over some polynomial ring R { \ displaystyle R.
Polynomial ring in n indeterminates over R / m.
Thus, the monic polynomials form a multiplicative semigroup of the polynomial ring A [ x ].
In particular, a polynomial ring over a GCD domain is also a GCD domain.
The universal formal group law coefficient ring ( Lazard 's universal ring ) is a polynomial ring.
Let formula 6 be a polynomial ring over the finite field formula 7.
Hilbert's basis theorem, in algebraic geometry, says that a polynomial ring over a Noetherian ring is Noetherian.
The polynomial ring is understood in the super sense, so if T has odd degree then T2 0.
Extending this example further, consider the polynomial ring in two variables, k, which has Krull dimension 2.
Of the polynomial ring GF ( p ) [ X ] by the ideal generated by P is a field of order q.
For example, the invariants of group number 4 form a polynomial ring with 2 generators of degrees 4 and 6.
Here A is a polynomial ring over a field, that is, A k.
In particular, the GK dimension of the polynomial ring k { \ displaystyle k } Is n.
For example, the polynomial ring k { \ displaystyle k } over a field k has dimension n.
Let R k { \ displaystyle R = k } be a polynomial ring over a field k.
They form a basis for the polynomial ring Z { \ displaystyle \ mathbb { Z } } in infinitely many variables.
For example, we may take A to be the polynomial ring F q { \ displaystyle F _ { q.
Its cohomology ring is Z, namely the free polynomial ring on a single 2-dimensional generator x ∈ H2.
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Examples of using Ring
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And place a ring upon her hand
Ring tones will not hold up in court
I had to go into the ring to finish it myself
Examples of using Polynomial
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A fourth order polynomial may be expressed as follows
A couple of students did not know what a polynomial was
The derivative of the polynomial is the polynomial
