Separative Ideals,Clean Elements,and Unit-Regularity

ABSTRACT

We prove that an ideal I of a regular ring R is separative if and only if each a ? R satisfying Rr(a)aR = Ra?(a)R = RaR(1 ? a)R ? I is unit-regular. If I is a separative ideal of a regular ring R, then each a ? R satisfying Rar(a²) = ?(a²)aR = R(a ? a²) R ? I is clean. Some applications are also obtained.     

Optimal Subgroups and Applications to Nilpotent Elements

Let G be a reductive group acting on an affine variety X, let x ∈ X be a point whose G-orbit is not closed, and let S be a G-stable closed subvariety of X which meets the closure of the G-orbit of x but does not contain x. In this paper we study G. R. Kempf’s optimal class Ω _G (x; S) of cocharacters of G attached to the point x; in particular, we consider how this optimality transfers to subgroups of G. Suppose K is a G-completely reducible subgroup of G which fixes x, and let H = C _G (K)⁰. Our main result says that the H-orbit of x is also not closed, and the optimal class Ω _H (x; S) for H simply consists of the cocharacters in Ω _G (x; S) which evaluate in H. We apply this result in the case that G acts on its Lie algebra via the adjoint representation to obtain some new information about cocharacters associated with nilpotent elements in good characteristic.     

Elements in Regular QB-Rings

In this article, we prove that every element in a regular QB-ring is the sum of an idempotent and a quasi-invertible element.     

Regular Elements in Quasi-Morphic Rings

We introduce, in this article, a partial order on quasi-morphic rings and investigate the behavior of regular elements in such rings. Further, the cleanness of regular elements in quasi-morphic rings having internal-cancelltion has been derived.     

Rings Whose Nilpotent Elements form a Levitzki Radical Ring

In this article, we first discuss the relations among JH^r = 0, JH^r?1·H = 0, and JH^r·x = 0. Then we give a counterexample to the question mentioned in the Remarks of [3 Cheng, C. C., Sakkalis, T., Wang, S. S. S. (1994). A case of the Jacobian conjecture. J. Pure and Applied Algebra 96:15–18.[Crossref], [Web of Science ®] , [Google Scholar]] and prove the equivalence among JH(x⁽¹⁾)JH(x⁽²⁾)…JH(x^(r)) = 0, JH(x⁽¹⁾)JH(x⁽²⁾)…JH(x^(r?1))·H(x^(r)) = 0, and JH(x⁽¹⁾)JH(x⁽²⁾)…JH(x^(r))·x^(r) = 0. Finally, we give partial answer to Conjecture 2 in [4 Connell, E., Zweibel, J. (1991). Exact and coexact matrices. J. Algebra 142:110–117.[Crossref], [Web of Science ®] , [Google Scholar]].     

Nilpotent Elements and Idempotents in Commutative Group Rings #

Flatness properties of acts over monoids and their connection with monoid amalgamation have been investigated for almost four decades and a substantial literature on the subject has now appeared. Analogous research, concerning the action of partially ordered monoids on partially ordered sets and its relation to pomonoid amalgamation, was begun in 1980s in two articles by S. M. Fakhruddin. The subject then remained dormant until the recent past when several articles on flatness in the setting of ordered monoids acting on posets (briefly, S-posets) appeared. It has now been established that the introduction of order results in severe restrictions as far as absolute flatness is concerned. Also, after formulating in the ordered context the Representation Extension and Right Congruence Extension Properties, first used by T. E. Hall to study semigroup amalgams, the authors recently observed in their article [4 Bulman-Fleming , S. , Nasir , S. ( 2010 ). Examples concerning absolute flatness and amalgamation in pomonoids . Semigroup Forum 80 : 272 – 292 .[Crossref], [Web of Science ®] , [Google Scholar]] that inverse monoids, though being amalgamation bases in the class of all monoids, may fail to possess this property when put in the ordered scenario. The purpose of the present article is to formulate an ordered version of the Strong Representation Extension Property of Hall and to explore its connections with absolute flatness and amalgamation of pomonoids. This enables us to prove that pogroups are (strong) amalgamation bases in the class of all pomonoids.     

多重胞元和规则多重分形

以超级分形纤维和双重分形纤维的研究结果为基础,达成了如下目标:首先,归纳、抽象出了多重胞元概念;其次,基于多重胞元概念,证实:具有严格自相似性的规则多重分形,不仅是可构造的,而且其构造模式具有普遍性;再者,通过分析构造模式,发现:任何规则多重分形,都可以在多重胞元意义下,被精确地等价成具有多重精细结构的广义单重分形．而基于这种等价性,单重分形维数公式就能够推广至规则多重分形维数公式,单重分形几何就能够推广至规则多重分形几何;最后,借助规则多重分形,构造了几种黄金分形．     

循环环的正则元

本文给出了循环环的所有正则元以及它们的数目 ,同时 ,给出了循环环是正则环的一个充要条件     

sl(3,κ)正则幂零表示投射模的Lowey序列

基域k是特征为5的代数闭域,李代数g=sl(3,k).当p-特征函数χ为正则幂零且具有标准Levi型时,本文得到了g的主不可分解模的Lowey序列及其单模自扩张的维数.     

Rational Wachspress-type Finite Elements on Regular Hexagons

This paperm concern finite-element methods for solving seconds-orderboundary-value elliptic problem. The principal result coverestimate of interpolatio error and, with conditionss on the"triangulation" of the domain, the effect of numerical intergrationwhen we use rational Watchspress-type finite elements on regularhexagons. A test between this method and that correspondingto polynomial finite of the same degree is indicated.     

On Finite Elements in Lattices of Regular Operators

Let E and F be vector lattices and the ordered space of all regular operators, which turns out to be a (Dedekind complete) vector lattice if F is Dedekind complete. We show that every lattice isomorphism from E onto F is a finite element in , and that if E is an AL-space and F is a Dedekind complete AM-space with an order unit, then each regular operator is a finite element in . We also investigate the finiteness of finite rank operators in Banach lattices. In particular, we give necessary and sufficient conditions for rank one operators to be finite elements in the vector lattice . A half year stay at the Technical University of Dresden was supported by China Scholarship Council.     

Invertible and Nilpotent Elements in the Group Algebra of a Unique Product Group

We describe the nilpotent and invertible elements in group algebras k[G] for k a commutative associative unital ring and G a unique product group, for example an ordered group.     

一类幂零矩阵幂零指标的特征

设(L, ,·)是一个incline. 本文给出了一个incline上幂零矩阵幂零指标的特征.其结果改进了文[4]中的相应结论.     

On the Finiteness of Noetherian Rings with Finitely Many Regular Elements

Let R be a left Noetherian ring and ZD(R) be the set of all zero-divisors of R. In this paper, it is shown that if R \ ZD(R) is finite, then R is finite.     

Homological Dimensions of the Algebra Formed by Entire Functions of Elements of a Nilpotent Lie Algebra

This note deals with homological characteristics of algebras of holomorphic functions of noncommuting variables generated by a finite-dimensional nilpotent Lie algebra . It is proved that the embedding of the universal enveloping algebra of into its Arens–Michael hull is an absolute localization in the sense of Taylor provided that      

On Regular Orbits of Elements of Classical Groups in Their Permutation Representations

Let H be a simple finite classical group not isomorphic to PSL(n, q) for any n, q. We prove that every cyclic subgroup of H has a regular orbit on every nontrivial permutation H-set.