On Modular Vector Invariant Fields

Let [Formula: see text] be a finite field of any characteristic and [Formula: see text] be the general linear group over [Formula: see text]. Suppose W denotes the standard representation of [Formula: see text], and [Formula: see text] acts diagonally on the direct sum of W and its dual space W∗. Let G be any subgroup of [Formula: see text]. Suppose the invariant field [Formula: see text], where [Formula: see text] in [Formula: see text] are homogeneous invariant polynomials. We prove that there exist homogeneous polynomials [Formula: see text] in the invariant ring [Formula: see text] such that the invariant field [Formula: see text] is generated by [Formula: see text] over [Formula: see text].

The Finite Element Desired Quantities Invariant Approximation Method in the Thin Shells Calculation Based on the Timoshenko Hypothesis

The displacement vector components vector (invariant) approximation implementation and the initial inclination angles by the hypothesis of S. P. Tymoshenko in obtaining the thin shell quadrangular finite element nodal forces stiffness matrix and the column is shown.

VECTOR INVARIANT IDEALS OF ABELIAN GROUP ALGEBRAS UNDER THE ACTION OF THE SYMPLECTIC GROUPS

Let F be a finite field and let Sp 2ν(F) be the symplectic group over F. If Sp 2ν(F) acts on the F-vector space F2ν, then it can induce an action on the vector space F2ν ⊕ F2ν, defined by (x, y)A = (xA, yA), ∀ x, y ∈ F2ν, A ∈ Sp 2ν(F). If K is a field with char K ≠ char F, then Sp 2ν(F) also acts on the group algebra K[F2ν ⊕ F2ν]. In this paper, we determine the structures of Sp 2ν(F)-stable ideals of the group algebra K[F2ν ⊕ F2ν] by augmentation ideals, and describe the relations between the invariant ideals of K[F2ν] and the vector invariant ideals of K[F2ν ⊕ F2ν].