splitting field


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splitting field

[′splid·iŋ ‚fēld]
(mathematics)
References in periodicals archive ?
3) F' is the splitting field of an irreducible polynomial of the form (1), for some u [member of] F.
Now, its is clear that, if y [member of] F, then F is the splitting field of [phi](T).
n] is the splitting field of the product of these polynomials, it is normal.
In other words, it belongs to the splitting field Q(i)([[[gamma].
Splitting Field and Wallett for second place was another Sunderland Harrier, Tom Doughty.
The company adopted a team-based tactic toward customer service by splitting field, office, and sales staff into cross-disciplinary teams of roughly 30 people each, who are responsible as a group for specific buyers.
For fixed exponent we are able to vary the index, and for fixed index we provide a lower and upper bound for the degree of a smallest abelian splitting field.
2], while n - m gives a measure of the ratio of the degree of the smallest abelian splitting field of D to the index of D (See the proposition in the next section).
6])-invariants in the covering space for the splitting field of the Mordell-Weil lattice of S[lambda] (or the Neron-Severi lattice of V[lambda]).
They introduce the theory of central simple algebras at a level accessible to graduate mathematics students, starting from scratch and including fundamental concepts such as splitting fields, Bayer group, crossed-product algebras, index and exponent, and algebras with involution.
He explains Galois theory, including such topics as splitting fields and their automorphisms, the characteristics of a field, derivation of a polynomial (multiple roots), the degree of an extension field, group characters, fundamental theorems and finite fields, then moves to polynomials with integral coefficients, including irreducibility and primitive roots of unity, and the theory of equations, including ruler and compass constructions, and the theorems of Steinitz and Abel.
They cover background from group theory, representations and modules, algebraic number theory, semi-simple rings and group algebras, group characters, induced characters, induced representations, non-smi-simple rings, Frobenius algebras, splitting fields and separable algebras, integral representations and modular representations.