Supersemiprime Rings and Supersemiprime Radical

In this paper,supersemiprime ring is introduced,relations among the supersemiprime rings and the some rings around it are discussed,supersemiprime radical and its properties are studied.

The Linear Combination of Derivations in Prime Rings

In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen. Our aim is to improve Niu's result. For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest.

Cocentralizing Generalized Derivations in Prime Rings

Let R be a prime ring with center Z and S包含 R. Two mappings D and G of R into itself are called cocentralizing on S if D（x）x - xG（x） ∈ Z for all x ∈S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime ease is also considered.

Notes on Automorphisms of Prime Rings

Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.

Generalized Derivations in Prime Rings

Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0.

Compositions of Generalized Derivations in Prime Rings

Let R be a prime ring with a non-central Lie ideal L. In the present paper we show that if the composition DG of two generalized derivations D and G is zero on L, then DG must be zero on R. And we get all the possibilities for the composition of a couple of generalized derivations to be zero on a non-central Lie ideal of a prime ring.

Annihilator on Co-commutators with Derivations on Lie Ideals in Prime Rings

Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a（d（u）u - ug（u）） = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d（x） = [p, x], and g（x） = -d（x） for some p in the Martindale quotient ring of R.

(Right)Partial Generalized Automorphisms of Semiprime Rings

In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.

Centralizing Automorphisms of Lie Ideals in Prime Rings of Characteristic 2

Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that \xσ, x] ∈Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R) = 2 and dimcRC = 4.

Left Annihilator of Power Values with Derivations on Lie Ideals in Prime Rings

Let R be a prime ring with characteristic di erent from two,d a derivation of R,L a noncentral Lie ideal of R,and a2R.In the present paper it is showed that if a(d(u^m)±u^m)^n for all u∈L,where m;n are xed positive integers,then a=0 unless R satis es s4,the standard polynomial identity in four variables.

立式自吸泵前口环几何参数对其自吸性能的影响

为探究立式自吸泵前口环几何参数对其自吸性能的影响,以350WFB-1200-50型外混式无密封立式自吸泵为研究对象,在保证自吸泵其他参数不变的情况下,通过改变前口环间隙δ和前口环长度l的数值大小,共设计20种方案.利用数值计算和试验验证相结合的研究方法,通过定常数值计算得到不同方案外特性曲线图及前口环进出口压差图;通过非定常数值计算得到不同方案不同时刻中间截面气体体积分布云图、不同方案自吸泵出口含气率变化图及不同方案自吸完成时间曲线图来研究立式自吸泵前口环几何参数与其自吸性能的关系.研究发现:前口环间隙δ和前口环长度l对自吸泵自吸性能均有影响,适当减小前口环间隙δ和增大前口环长度l均能提高自吸泵自吸性能,且当前口环间隙δ过大时,其对自吸泵自吸性能的影响大于前口环长度l对自吸泵自吸性能的影响.

液环式航空燃油离心泵自吸性能

基于Mixture模型对液环式航空燃油泵进行自吸阶段的非稳态数值计算,研究自吸过程中燃油泵内气液两相分布的变化过程,对不同时刻下燃油泵内部含气率、气液两相分布、压力及速度流线、熵产率和湍动能变化规律进行分析.结果表明:燃油泵的吸气和排气主要集中在自吸过程的前期和中期;随着自吸时间的增加,各监测面的含气率逐渐降低,当自吸时间为3.00 s时,蜗壳出口含气率接近于0,自吸过程结束;泵内压力随相对距离的增加而增大,泵内同一相对距离平面压力随自吸时间的增加而增大;在气液混合时,高速区域主要集中在叶轮中间流道和蜗壳壁面处,低速区域则集中分布在隔舌附近和导叶出口;随着自吸过程的进行,泵内湍动能和熵产率也随之增大,泵内能量损失增大,主要集中在叶轮叶片、导叶叶片和蜗壳出口处.

Redefined generalized fuzzy ideals of near-rings

With a new idea, we redefine generalized fuzzy subnear-rings （ideals） of a near- ring and investigate some of its related properties. Some new characterizations are given. In particular, we introduce the concepts of strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings, and discuss the relationship between strong prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals and prime （or semiprime） （∈, ∈∨ q）-fuzzy ideals of near-rings.

关于Primely Polar环

称环R中的元素a是primely polar的,如果存在p^2=p∈comm^2(a)使得a+p∈U(R)且ap∈P(R).称环R是primely polar的,如果环R中每个元素都是primely polar的.文章将primely polar环与其他熟悉的环理论建立起联系,证明了交换的强π正则环是primely polar的,以及primely polar环是强π正则环.此外,还研究了primely polar环在Drazin逆中的特性.结论表明,一个环R是primely polar的,当且仅当对任意的a∈R,存在e^2=e∈comm(a)使得a-e∈U(R),ae∈P(R),当且仅当对任意的a∈R,存在b∈comm(a)使得b=b^2a,a-a^2b∈P(R).

TOPOLOGICAL CHARACTERIZATIONS OF THE EXTENDING PROPERTY OF RINGS

A commutative ring R is called extending if every ideal is essential in a direct summand of RR. The following results are proved： （1） C（X） is an extending ring if and only if X is extremely disconnected; （2） Spec（R） is extremely disconnected and R is semiprime if and only if R is a nonsingular extending ring; （3） Spec（R） is extremely disconnected if and only if R/N（R） is an extending ring, where N（R） consists of all nilpotent elements of R. As an application, it is also shown that any Gelfand nonsingular extending ring is clean.

On a Characterization of Quasi-valuation Rings

Let R be a commutative ring without nil-factor. In this paper, we discuss the problem of quasi-valuation ring presented in the reference 'Wang Shianghaw, On quasi-valuation ring, Northeast People's Univ. Natur. Sci. J., (1)(1957), 27-40', when the quotient field of R is an algebraic number field or an algebraic function field, and we obtain a characterization of quasi-valuation rings.

素环上的广义(θ,θ)-导子

R是2-扭自由素环,Z(R)是R的中心,J是R的非零Jordan理想,F是R的广义(θ,θ)-导子,d是F的伴随(θ,θ)-导子.若对任意的u,v∈J,F满足以下条件之一:(ⅰ)F(u°v)=0,(ⅱ)F(u°v)=θ(u°v),(ⅲ)F(u°v)=θ([u,v]),则d=0或J■Z(R).

带有对合的素环的微分恒等式

Let R be a prime ring of characteristic different from two with the second involution∗andαan automorphism of R.An additive mapping F of R is called a generalized(α,α)-derivation on R if there exists an(α,α)-derivation d of R such that F(xy)=F(x)α(y)+α(x)d(y)holds for all x,y∈R.The paper deals with the study of some commutativity criteria for prime rings with involution.Precisely,we describe the structure of R admitting a generalized(α,α)-derivation F satisfying any one of the following properties:(i)F(xx∗)−α(xx∗)∈Z(R),(ii)F(xx∗)+α(xx∗)∈Z(R),(iii)F(x)F(x∗)−α(xx∗)∈Z(R),(iv)F(x)F(x∗)+α(xx∗)∈Z(R),(v)F(xx∗)−F(x)F(x∗)∈Z(R),(vi)F(xx∗)−F(x∗)F(x)=0 for all x∈R.Also,some examples are given to demonstrate that the restriction of the various results is not superfluous.In fact,our results unify and extend several well known theorems in literature.

素环上广义(θ,θ)-导子的性质

设R是2-扭自由素环,Z(R)是R的中心,U是R的平方封闭Lie理想,F,G是R的广义(θ,θ)-导子,d,h是其伴随(θ,θ)-导子.若对任意的u,v∈U,F,G满足以下条件之一:(1)F(u)θ(u)=±θ(u)G(u),(2)[F(u),θ(v)]=±[θ(u),G(v)],(3)[F(u),θ(v)]=±θ(u)°G(v),则U⊂Z(R).

群环Z_nG的代数性质及其结构

讨论了群环ZnG的代数性质及其结构,对群环ZnG的素谱和零因子给出了较为具体的刻画。