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Some Related Sentences
Every and polynomial
Every root of
a polynomial equation whose coefficients are algebraic numbers
is again algebraic
.
Every polynomial P in
x corresponds to
a function, ƒ (
x )
Every output of an encoder can be described by its own transfer function, which
is closely related to the generator
polynomial.
* Every root of
a monic
polynomial whose coefficients are algebraic integers
is itself an algebraic integer
.
Every polynomial in can be factorized into polynomials that are irreducible over F
. This factorization
is unique up to permutation of the factors and the multiplication of the factors by nonzero constants from F ( because the
ring of polynomials over
a field
is a unique factorization domain whose units are the nonzero constant polynomials ).
Every delta operator ' has
a unique sequence of " basic polynomials ",
a polynomial sequence defined by three conditions:
Every real
polynomial of odd degree has at least one real number as
a root
.
* Every irreducible closed subset of P
< sup
> n </ sup >( k ) of codimension one
is a hypersurface ; i
. e., the zero set of some homogeneous
polynomial.
* Every Jacobi-like
polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality
is, and has Q
* Every Laguerre-like
polynomial sequence can have its domain shifted, scaled, and / or reflected so that its interval of orthogonality
is, and has Q =
* Every Hermite-like
polynomial sequence can have its domain shifted and / or scaled so that its interval of orthogonality
is, and has Q
Every polynomial function
is a rational function with
.
* Every irreducible
polynomial over k has distinct roots
.
* Every polynomial over k
is separable
.
Every field and every
polynomial ring over
a field ( in arbitrarily many variables )
is a reduced
ring.

In mathematics, an integer-valued
polynomial ( also known as
a numerical
polynomial ) P ( t )
is a polynomial whose value P (
n )
is an integer for every integer
n. Every polynomial with integer coefficients
is integer-valued, but the converse
is not true
.
* Every irreducible
polynomial in K which has
a root in L factors into linear factors in L
.
Every and ring

**
Every unital
ring other than the trivial
ring contains
a maximal ideal
.
Every Boolean algebra ( A, ∧, ∨) gives rise to
a ring ( A, +, ·) by defining
a + b := (
a ∧ ¬ b ) ∨ ( b ∧ ¬
a ) = (
a ∨ b ) ∧ ¬(
a ∧ b ) ( this operation
is called symmetric difference in the case of sets and XOR in the case of logic ) and
a · b :=
a ∧ b
. The zero element of this
ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the
ring is the 1 of the Boolean algebra
.

In Norse mythology, Draupnir ( Old Norse " the dripper ")
is a gold
ring possessed by the god Odin with the ability to multiply itself:
Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original
.
Every module over
a division
ring has
a basis ; linear maps between finite-dimensional modules over
a division
ring can be described by matrices, and the Gaussian elimination algorithm remains applicable
.
Every division
ring is therefore
a division algebra over its center
.
Every objective has
a different size
ring, so for every objective another condenser setting has to be chosen
.
Every match must be assigned
a rule keeper known as
a referee, who
is the final arbitrator ( In multi-man lucha libre matches, two referees are used, one inside the
ring and one outside ).
* In any
ring R,
a maximal ideal
is an ideal M that
is maximal in the set of all proper ideals of
R, i
. e
. M
is contained in exactly 2 ideals of
R, namely M itself and the entire
ring R. Every maximal ideal
is in fact prime
.
* Krull's theorem ( 1929 ):
Every ring with
a multiplicative identity has
a maximal ideal
.
Every Boolean
ring R satisfies
x ⊕
x
Every prime ideal P in
a Boolean
ring R is maximal: the quotient
ring R / P
is an integral domain and also
a Boolean
ring, so it
is isomorphic to the field F
< sub > 2
</ sub >, which shows the maximality of P
. Since maximal ideals are always prime, prime ideals and maximal ideals coincide in Boolean rings
.
Every finitely generated ideal of
a Boolean
ring is principal ( indeed, (
x, y )=(
x + y + xy )).
* Every finitely-generated
commutative algebra over
a commutative Noetherian
ring is Noetherian
.
* Every localization of
a commutative Noetherian
ring is Noetherian
.
Every topological
ring is a topological group ( with respect to addition ) and hence
a uniform space in
a natural manner
.
Every prostaglandin contains 20 carbon atoms, including
a 5-carbon
ring.
Every and R
* Every rectangle
R is in M
. If the rectangle has length h and breadth k then
a (
R ) =
Every holomorphic function can be separated into its real and imaginary parts, and each of these
is a solution of Laplace's equation on
R < sup
> 2
</ sup >.
Every vector v in determines
a linear map from
R to taking 1 to v, which can be thought of as
a Lie algebra homomorphism
.
Every binary relation
R on
a set S can be extended to
a preorder on S by taking the transitive closure and reflexive closure,
R < sup >+=</ sup >.
* Every separable metric space
is isometric to
a subset of C (), the separable Banach space of continuous functions →
R, with the supremum norm
.
Every simple R-module
is isomorphic to
a quotient
R / m where m
is a maximal right ideal of
R. By the above paragraph, any quotient
R / m
is a simple module
.
Every random vector gives rise to
a probability measure on
R < sup
> n </ sup
> with the Borel algebra as the underlying sigma-algebra
.
* Every left ideal I in
R is finitely generated, i
. e
. there exist elements
a < sub > 1
</ sub >,
..., a < sub > n </ sub > in I such that I = Ra
< sub > 1
</ sub > + ... + Ra
< sub > n </ sub >.
* Every non-empty set of left ideals of
R, partially ordered by inclusion, has
a maximal element with respect to set inclusion
.
Every year since 1982, the W
. C
. Handy Music Festival
is held in the Florence / Sheffield / Muscle Shoals area, featuring blues, jazz, country, gospel, rock music and
R & B
.
Every adult citizen of this small settlement signed the small petition ; E
. K Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and
R. H
. Valentine
.
Every smooth submanifold of
R < sup
> n </ sup
> has an induced Riemannian metric g: the inner product on each tangent space
is the restriction of the inner product on
R < sup
> n </ sup >.
0.219 seconds.