具有幂零局部子群的有限群

一个有限非幂零群G称为PN-群,如果NG(P)是幂零的,对于每个素数p和每个满足P(∈)Z∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理.     

具有幂零局部子群的有限群

一个有限非幂零群G称为PN-群,如果NC(P)是幂零的,对于每个素数p和每个满足PZ∞(G)的非正规子群p-子群P.本文将给出可解PN-群的结构和一些特征定理.     

COMMUTATIVE RINGS WITH FINITE QUOTIENT FIELDS

Abstract

We consider the class of all commutative reduced rings for which there exists a finite subset T ? A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for this class of rings,and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals.     

ASYMPTOTIC PROPERTIES OF ELEMENTS IN GROUP RINGS OF FINITE GROUPS

A relation between algebraic degrees of eigenvalues of an element in the group ring Z G of a finite group G and their multiplicities is obtained. This result can be regarded as a theorem on asymptotic behavior of parameters in group rings of finite groups which is a parallel result of several well known theorems concerning the relationships of parameters in finite groups.     

RINGS WITH INVLOUTION WHOSE SYMMETRIC ELEMENTS ARE G-INVERTIBLE

This paper investigates structure theorems for some types of rings with involution in which for every symmetric element s there exists a symmetric element t such that st=ts, $\[s = {s^2}t\]$.     

TORSION-FREE ABELIAN GROUPS WITH FINITE RANK ENDOMORPHISM RINGS

Abstract

We show that if A and C are torsion-free abelian groups with ∩{ker f|f: A → C} = 0 = ∩{ker g|g: C → A}, and if A has a left Artinian quasi-endomorphism ring then A and C share a nonzero quasi-summand. Some consequences explored.     

NIL PROBLEMS REVISITED FOR ALMOST NILPOTENT RINGS

Abstract

We begin with the notion of K-flat projectivity. For each biframe L we then introduce a binary relation ?L on it. The K-flat projective biframes are exactly such biframes with each element a of the total (first, second) part approximated by the elements x of the total (first, second) part, x?_L a and the relation ?_L being stable wrt. the meet operation on L. Further on, we introduce the notion of a K-comonad and characterize K-flat projective biframes as those biframes having a coalgebra structure for the K-comonad. The K-coherent biframes and K-flat projective biframes are coreflective in all biframes.     

具有很多素数阶元的有限群

考察元素的阶如何影响有限群的结构是群论中的一个重要课题．本文研究存在一个正规子群N，N外的元素都是素数阶元的有阶群．主要利用熟知的Thompson的一个定理，获得了这样的有限群．     

有限置换模自同态环的可分性质

设Q是有限置换右R模,则EndR(Q)是可分环当且仅当对所有A,B∈FP(Q),A A≌A B≌B B A≤ B或B≤ A.作为应用得到了EndR(P Q)是可分环当且仅当EndRP和EndRQ为可分环,其中P,Q为有限置换右R模.     

有限置换模自同态环的可分性质

设Q是有限置换右R模,则End_R(Q)是可分环当且仅当对所有A,B∈FP(Q),A AA B B B A≤ B或 B≤A,作为应用得到了 End_R(P Q)是可分环当且仅当End_R P和End_R Q为可分环,其中P,Q为有限置换右R模。     

A LOCALLY FINITE VARIETY OF RINGS WITH AN UNDECIDABLE EQUATIONAL THEORY

We prove that the non-finitely based system of polynomial identitiesover an arbitrary field of characteristic 2 given by Gupta and Krasilnikov in [A non-finitelybased system of polynomial identities which contains the identityx⁶ = 0, Quart. J. Math. 53 (2002), 173–183] can, by aslight modification, be turned into an independent system. Thishas important consequences for algorithmic problems in algebra:there is a locally finite-dimensional variety of associativealgebras (and, in particular, a locally finite variety of rings)that has an undecidable equational theory. For such a variety,the uniform word problem is unsolvable, and yet the word problemis recursively solvable for each individual finitely presentedalgebra (ring) in that variety.     

分次环的有限正规张

本文研究了群分次环的有限正规分次扩张问题.利用经典环论方法,得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系,同时,给出了分次情形的Cutting down定理和Lying over定理.     

最高阶元个数是4p的有限群

本文证明了如果有限群G恰有4p个最高阶元,p为素数,则群G为可解群,除非G同构于S5.     

最高阶元个数是4p的有限群

本文证明了如果有限群G恰有4p个最高阶元,p为素数,则群G为可解群,除非G同构于S5.     

FINITE ELEMENTS WITH LOCAL PROJECTION STABILIZATION FOR INCOMPRESSIBLE FLOW PROBLEMS

In this paper we review recent developments in the analysis of finite element methods for incompressible flow problems with local projection stabilization （LPS）. These methods preserve the favourable stability and approximation properties of classical residual-based stabilization （RBS） techniques but avoid the strong coupling of velocity and pressure in the stabilization terms. LPS-methods belong to the class of symmetric stabilization techniques and may be characterized as variational multiscale methods. In this work we summarize the most important a priori estimates of this class of stabilization schemes developed in the past 6 years. We consider the Stokes equations, the Oseen linearization and the NavierStokes equations. Furthermore, we apply it to optimal control problems with linear（ized） flow problems, since the symmetry of the stabilization leads to the nice feature that the operations ＂discretize＂ and ＂optimize＂ commute.     

分次环的有限正规扩张

本文研究了群分次环的有限正规分次扩张问题．利用经典环论方法，得到一个群分次环与其有限正规分次扩张环之间关于分次Jacobson根和分次素根的关系，同时，给出了分次情形的Cutting down定理和Lying over定理．     

SURFACE FINITE ELEMENTS FOR

In this article we define a surface finite element method （SFEM） for the numerical solution of parabolic partial differential equations on hypersurfaces F in R^n＋1. The key idea is based on the approximation of F by a polyhedral surface Гh consisting of a union of simplices （triangles for n = 2, intervals for n = 1） with vertices on Г. A finite element space of functions is then defined by taking the continuous functions on Гh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Г. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward. We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demorrstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.     

QUADRILATERAL FINITE ELEMENTS FOR PLANAR LINEAR ELASTICITY PROBLEM WITH LARGE LAME CONSTANT

1.PlanarlinearelasticityproblemThetwo--dimellsionallinearelasticityproblemassociatedwithahomogeneousisotropicelasticmaterialwithpuredisplacementscanbemodelledbythefollowingellipticboundaryvalueproblem:wherefiCWZisanopenandboundeddomain,if=(ul,u2)thedisplacement,f(x)thebodyforce,andA,ptheLameconstants.Differentequivalentformulationsof(1.1)-(1.2)canbefoundin[3,4,if].ItiswellknownthattheconvergencerateforthestandarddisplacementmethodusingcontinuouslinearfiniteelementsdeterioratesastheLameconsta…     

有限群分次环上的余挠对研究

本文研究了余挠对在有限群分次和非分次情况下的联系.利用分次理论以及相对同调,我们首先研究了R是任意环G是有限群的情况下,余挠对在R-模范畴以及斜群环S=R*G-模范畴之间的关系;然后我们研究了R-gr范畴中刚性余挠对的等价刻画,同时给出了余挠对在R-gr范畴与R-模范畴之间的关系,其中R是G分次环,群G是有限群且|G|^-1∈R.     

GRADED RINGS OF LOCAL FINITE REPRESENTATION TYPE

Abstract

Graded Artin algebras whose category of graded modules is locally of finite representation type are introduced. The representation theory of such algebras is studied. In the hereditary case and in the stably equivalent to hereditary case, such algebras are classified.