Abstract. Let Fq be a finite field, Fqs be an extension of Fq, let f(x) ∈ Fq[x] be a polynomial of degree n with gcd(n, q) = 1. We present a recursive formula for evaluating the exponential sum ∑ c∈Fqs χ(s)(f(x)). Let a and b be two elements in Fq with a 6= 0, u be a positive integer. We obtain an estimate for the exponential sum ∑ c∈F qs χ(s)(acu + bc−1), where χ(s) is the lifting of an additi...

In [8] we introduced the notion of a local torus actions modeled on the standard representation (we call it a local torus action for simplicity), which is a generalization of a locally standard torus action. In this note we define a lifting of a local torus action to a principal torus bundle, and show that there is an obstruction class for the existence of liftings in the first cohomology of th...

Recall that an algebraic module is aKG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that non-periodic algebraic modules are very rare, and that if the complexity of an algebraic module is at least 3, then it is the only algebraic module on its component of the (stable) Auslander–Re...

In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...

In this paper we show that a direct decomposition of modules M N, with N homologically independent to the inJective hull of H, is a CS-module if and only if N is injective relative to H and both of M and N are CS-modules. As an application, we prove that a direct sum of a non-singular semisimple module and a quasi-continuous module with zero socle is quasi-continuous. This result is known for q...

Let V be a G-module where G is a complex reductive group. Let Z := V//G denote the categorical quotient and let π : V → Z be the morphism dual to the inclusion O(V ) ⊂ O(V ). Let φ : Z → Z be an algebraic automorphism. Then one can ask if there is an algebraic map Φ: V → V which lifts φ, i.e., π(Φ(v)) = φ(π(v)) for all v ∈ V . In Kuttler [Kut11] the case is treated where V = rg is a multiple of...

Winkler (1988) and Pauer (1992) present algorithms for a Hensel lifting of a modular Gröbner basis over lucky primes to a rational one. They have to solve a linear system with modular polynomial entries that requires another (modular) Gröbner basis computation. After an extension of luckiness to arbitrary (commutative noetherian) base rings we show in this paper that for a homogeneous polynomia...

Letting n≥2k, the partition algebra CAk≥2(n) has two one-dimensional subrepresentations that correspond in a natural way to alternating and trivial characters of symmetric group Sk. In 2019, Benkart Halverson introduced proved evaluations distinguished bases CAk(n) for nonzero elements regular CAk(n)-submodule corresponds Young symmetrizer ∑σ∈Skσ; 2016, Xiao an explicit formula analogue sign re...

Recent researches have shown that the adaptive directional lifting (ADL) can represent edges and textures in images effectively. This makes it possible to separate noise from image signal distinctly in image denoising. However, a key issue named orientation estimation for ADL becomes inefficient and error prone in the noised circumstance. The authors propose a robust adaptive directional liftin...

let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...