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。

ON VALUE DISTRIBUTIONS OF GENERAL DIFFERENTIAL MONOMIALS

Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0】2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.

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.

Pseudo Laguerre Matrix Polynomials, Operational Identities and Quasi-Monomiality

The main purpose of this paper is to introduce the matrix extension of the pseudo Laguerre matrix polynomials and to explore the formal properties of the operational rules and the principle of quasi-monomiality to derive a number of properties for pseudo Laguerre matrix polynomials.

Colon Structure of Associated Primes of Monomial Ideals

We find an explicit expression of the associated primes of monomial ideals as a colon by an element,using the unique irredundant irreducible decomposition whose irreducible components are monomial ideals.An algorithm to compute is given using Macaulay2.For squarefree monomial ideals the problem is related to the combinatorics of the underlying clutter or graph.For ideals of Borel type,the monomial u takes a simpler form,and we classify when is unique.

On the Unique Minimal Monomial Basis of Birkhoff Interpolation Problem

This paper studies the minimal monomial basis of the n-variable Birkhoff interpolation problem. First, the authors give a fast B-Lex algorithm which has an explicit geometric interpretation to compute the minimal monomial interpolation basis under lexieographie order and the algorithm is in fact a generalization of lex game algorithm. In practice, people usually desire the lowest degree interpolation polynomial, so the interpolation problems need to be solved under, for example, graded monomial order instead of lexicographie order. However, there barely exist fast algorithms for the non- lexicographic order problem. Hence, the authors in addition provide a criterion to determine whether an n-variable Birkhoff interpolation problem has unique minimal monomial basis, which means it owns the same minimal monomial basis w.r.t, arbitrary monomial order. Thus, for problems in this case, the authors can easily get the minimal monomial basis with little computation cost w.r.t, arbitrary monomial order by using our fast B-Lex algorithm.

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.

On monomial linearisation and supercharacters of pattern subgroups

Column closed pattern subgroups U of the finite upper unitriangular groups U_n(q) are defined as sets of matrices in U_n(q) having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction of monomial linearisation in his thesis and apply this to CU yielding a generalisation of Yan's coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters,by describing the resulting orbits and determining the Hom-spaces between orbit modules.

Squarefree Monomial Modules and Extremal Betti Numbers

Let K be a field and let S = K[x1,...,xn] be a polynomial ring over K. Let F = ir=1 Sei be a finitely generated graded free S-module with basis {e1,..., er} in degrees f1,..., fr such that f1≤ f2 ~≤……≤ fr. We examine some classes of squarefree monomial submodules of F. Hence, we focalize our attention on the Betti table of such classes in order to analyze the behavior of their extremal Betti numbers.

Tight monomials for type B3

The global crystal basis or canonical basis plays an important role in the theory of the quantized enveloping algebras and their representations. The tight monomials are the simplest elements in the canonical basis. We discuss the tight monomials in quantized enveloping algebra of type B3.

Castelnuovo-Mumford regularity and projective dimension of a squarefree monomial ideal

Let S = K[x1, x2,..., xn] be the polynomial ring in n variables over a field K, and let I be a squarefree monomial ideal minimally generated by the monomials ul,u2,...,Um. Let w be the smallest number t with the property that for all integers 1 ≤ i1 〈 i2 〈 … 〈 it ≤ m such that lcm（uil, ui2,..., uii） = lcm（ul,u2,...,Um）. We give an upper bound for Castelnuovo-Mumford regularity of I by the bigsize of I. As a corollary, the projective dimension of I is bounded by the number w.

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).