三角Monomial代数的张量积

考虑三角monomial代数的张量积及其箭图刻画.进一步地,通过箭图表示,讨论代数A、B与扩张代数A kB之间模的关系,包括不可分解模、投射模、内射模、平坦模等.

Monomial拟遗传代数的好模范畴

用图表示的两个子范畴及其性质，研究ｍｏｎｏｍｉａｌ代数及其上的拟遗传代数的好模范畴，余好模范畴，及特征模。主要结论给出了Ａ是ｍｏｎｏｍｉａｌ代数及Ｆ（Δ）＝ｒｅｐ１≤（Ｑ，Ｉ）的刻划及其对偶结论。

Monomials with t-value ≤ 6 in Canonical Basis of Quantized Enveloping Algebra of Type B3

All monomials with t-value ≤ 6 in Canonical basis of quantized enveloping algebra of type B3 are determined in this paper.

A note on the perturbed monomial mapping

In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r > 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.

Monomial Derivations without Darboux Polynomials

In this paper, it is proved that a monomial derivation d of k[x, y, z] has no Darboux polynomials if and only if d is a strict derivation with a trivial ring of constants, and we give the specific conditions when it has no Darboux polynomials.

Batalin-Vilkovisky Structure on Hochschild Cohomology of Self-Injective Quadratic Monomial Algebras

We give a complete description of the Batalin-Vilkovisky algebra structure on Hochschild cohomology of the self-injective quadratic monomial algebras.

Tight Monomials in Quantum Group for Type <i>A</i>₅with <i>t</i>≤ 6

All tight monomials in quantum group for type A5 with t ≤ 6 are determined in this paper.

Tight Monomials with t-Value ≤ 9 for Quantum Group of Type D₄

All monomials with t-value ≤9 in Canonical basis of quantum group for type D4 are determined in this paper.

Monomial Hopf algebras over fields of positive characteristic

In this paper, we study the structures of monomial Hopf algebras over a field of positive characteristic. A necessary and sufficient condition for the monomial coalgebra Cd(n) to admit Hopf structures is given here, and if it is the case, all graded Hopf structures on Cd(n)are completely classified. Moreover, we construct a Hopf algebras filtration on Cd(n) which will help us to discuss a conjecture posed by Andruskiewitsch and Schneider. Finally combined with a theorem by Montgomery, we give the structure theorem for all monomial Hopf algebras.

Zeros of Monomial Brauer Characters

Let G be a finite group and p be a fixed prime. A p-Brauer character of G is said to be monomial if it is induced from a linear p-Brauer character of some subgroup(not necessarily proper) of G. Denote by IBr_m(G) the set of irreducible monomial p-Brauer′characters of G. Let H = G′O^p′(G) be the smallest normal subgroup such that G/H is an abelian p′-group. Suppose that g ∈ G is a p-regular element and the order of gH in the factor group G/H does not divide |IBr_m(G)|. Then there exists ? ∈ IBr_m(G) such that ?(g) = 0.

Commutators and Semi-commutators of Monomial Toeplitz Operators on the Pluriharmonic Hardy Space

In this paper,the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere.As a consequence,many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.

Normal Sylow subgroups and monomial Brauer characters

Let G be a finite group,p be a prime divisor of|G|,and P be a Sylow p-subgroup of G.We prove that P is normal in a solvable group G if|G:kerφ|_(p′)=φ(1)_(p′)for every nonlinear irreducible monomial p-Brauer characterφof G,where kerφis the kernel ofφandφ(1)_(p′)is the p′-part ofφ(1).

Complete Intersection Monomial Curves and the Cohen-Macaulayness of Their Tangent Cones

Let C(n)be a complete intersection monomial curve in the 4-dimensional affine space.In this paper we study the complete intersection property of the monomial curve C(n+wv),where w>0 is an integer and v ∈ N^4.In addition,we investigate the Cohen-Macaulayness of the tangent cone of C(n+wv).

Armendariz Property of k[x,y]Modulo Monomial Ideals

In this paper,we give equivalent conditions for the factor rings of the polynomial ring k[x,y]modulo monomial ideals to be Armendariz rings,where k is a field.For an ideal I with 2 or 3 monomial generators,or n homogeneous monomial generators,such that k[x,y]/I is an Armendariz ring,we characterize the minimal generator set G(I)of I.

拟遗传代数的一种判定方法

利用[1]中引进的图表示的两个子范畴,给出拟遗传代数的一种判定方法。

加密数据上的计算密码学技术研究综述

近年来机密数据被盗事件在国内外时有发生,其所带来的经济损失和社会影响持续加剧。尽管已有系统采取了若干安全措施,然而经验表明,攻击者往往能够通过各种方式攻入系统,盗取用户数据。为了从根本上保护数据机密性,应确保即使攻击者能够获取存储在服务器上数据的访问权限,数据机密性依然不受到威胁,即数据以加密形式存储在服务器上;另外,为了保持数据的可用性,应允许服务器在密文上进行计算。针对支持在加密数据上计算的密码学技术,如同态加密、函数加密、可搜索加密以及CryptDB和Monomi等应用系统进行了综述性介绍,并指出有待解决的关键问题和未来的研究方向。

Certain Results for the 2-Variable Peters Mixed Type and Related Polynomials

In this article, the 2-variable general polynomials are taken as base with Peters polynomials to introduce a family of 2-variable Peters mixed type polynomials.These polynomials are framed within the context of monomiality principle and their properties are established. Certain summation formulae for these polynomials are also derived. Examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored.

A Characterization of Sequentially Cohen-Macaulay Matroidal Ideals

Let R=K[x1,…,xn]be the polynomial ring in n variables over a field K and I be a matroidal ideal of R.We show that I is sequentially Cohen-Macaulay if and only if the Alexander dual Iy has linear quotients.As a consequence,I is sequentially Cohen-Macaulay if and only if I is shellable.

Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an infinite number of variables. We adopt von Koch and Hilbert’s definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants.Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.

Characteristic modules and tensor products over quasi-hereditary algebras

Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.