Splitting field information

In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial...

oxidation state. A higher oxidation state leads to a larger splitting relative to the spherical field. the arrangement of the ligands around the metal ion....

Splitting, railway operation Heegaard splitting Splitting field Splitting principle Splitting theorem Splitting lemma for the numerical method to solve...

Zero field splitting (ZFS) describes various interactions of the energy levels of a molecule or ion resulting from the presence of more than one unpaired...

the ligand-field splitting parameter in ligand field theory, or the crystal-field splitting parameter in crystal field theory. The splitting parameter...

P form a field of order q, which is equal to F by the minimality of the splitting field. The uniqueness up to isomorphism of splitting fields implies thus...

call a field E a splitting field for A over K if A⊗E is isomorphic to a matrix ring over E. Every finite dimensional CSA has a splitting field: indeed...

extension. For finite extensions, a normal extension is identical to a splitting field. Let L / K {\displaystyle L/K} be an algebraic extension (i.e., L is...

along the same lines that for any subset S of K[x], there exists a splitting field of S over K. An algebraic closure Kalg of K contains a unique separable...

R/m, which is a field. Frequently, R is a local ring and m is then its unique maximal ideal. In abstract algebra, the splitting field of a polynomial...

normal extension and a separable extension. E {\displaystyle E} is a splitting field of a separable polynomial with coefficients in F . {\displaystyle F...

above construction, one can construct a splitting field of any polynomial from K[X]. This is an extension field L of K in which the given polynomial splits...

[ˈzeːmɑn]) is the effect of splitting of a spectral line into several components in the presence of a static magnetic field. It is named after the Dutch...

field extension is the following: Given a polynomial f ( x ) ∈ F [ x ] {\displaystyle f(x)\in F[x]} , let E / F {\displaystyle E/F} be its splitting field...

splitting is the chemical reaction in which water is broken down into oxygen and hydrogen: 2 H2O → 2 H2 + O2 Efficient and economical water splitting...

theorem of Galois theory, which proves that the fields lying between the ground field and the splitting field are in one-to-one correspondence with the subgroups...

same number of preimages. The splitting of primes in extensions that are not Galois may be studied by using a splitting field initially, i.e. a Galois extension...

separable). If L is the field extension K(T 1/p) (the splitting field of P) then L/K is an example of a purely inseparable field extension. In L ⊗ K L {\displaystyle...

In the mathematical field of geometric topology, a Heegaard splitting (Danish: [ˈhe̝ˀˌkɒˀ] ) is a decomposition of a compact oriented 3-manifold that...

measure the sign and strength of this electric field gradient, which is affected by the chemical environment of the nuclei. Electric quadrupole splitting...

{\displaystyle \{1,\alpha ,\ldots ,\alpha ^{n-1},\alpha ^{n}\}} ). If L is a splitting field of f ( X ) {\displaystyle f(X)} containing its n distinct roots α 1...

simplest case where the Galois group is not abelian. Consider the splitting field K of the irreducible polynomial x 3 − 2 {\displaystyle x^{3}-2} over...

magnetic field. The Stark effect – splitting because of an external electric field. In physical chemistry: The Jahn–Teller effect – splitting of electronic...

In the mathematical field of differential geometry, there are various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric...

the splitting field M of P has Galois group G over L, and such that every extension K/F with Galois group G can be obtained as the splitting field of a...

primitive cube root of unity). For a field containing all the roots of a polynomial, see Splitting field. A rupture field of X 2 + 1 {\displaystyle X^{2}+1}...