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共有20条相似文献,以下是第1-20项 搜索用时 78 毫秒

1.  On JB-Rings  
   Huanyin CHEN Department of Mathematics  Hunan Normal University  Changsha 410006  China.《数学年刊B辑(英文版)》,2007年第28卷第6期
   A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2.    

2.  On Weakly Semicommutative Rings  
   CHEN WEI-XING    CUI SHU-YING《东北数学》,2011年第2期
   A ring R is said to be weakly semicommutative if for any a,b∈R, ab=0 implies aRb(?)Nil(R),where Nil(R) is the set of all nilpotent elements in R. In this note,we clarify the relationship between weakly semicommutative rings and NI-rings by proving that the notion of a weakly semicommutative ring is a proper generalization of NI-rings.We say that a ring R is weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical,and prove that if R is a weakly 2-primal ring which satisfiesα-condition for an endomorphismαof R(that is,ab=0(?)aα(b)=0 where a,b∈R) then the skew polynomial ring R[x;α] is a weakly 2-primal ring,and that if R is a ring and I is an ideal of R such that I and R/I are both weakly semicommutative then R is weakly semicommutative. Those extend the main results of Liang et al.2007(Taiwanese J.Math.,11(5)(2007), 1359-1368) considerably.Moreover,several new results about weakly semicommutative rings and NI-rings are included.    

3.  分次单环的结构  
   朱彬《东北数学》,2003年第19卷第3期
   A characterization of gr-simple rings is given by using the notion of componentwise-dense subrings of a full matrix ring over a division ring. As a consequence, any G-graded full matrix ring over a division ring is isomorphic to a dense subring of a full matrix ring with a good G-grading. Some conditions for a grading of a full matrix ring to be isomorphic to a good one are given, which generalize some results in: Dascascu, S., Lon, B., Nastasescu, C. and Montes, J. R., Group gradings on full matrix rings, J. Algebra, 220(1999), 709-728.    

4.  Generalized Differential Identities of (Semi-)Prime Rings  
   Feng WEI《数学学报(英文版)》,2005年第21卷第4期
   Let R be a semiprime ring with characteristic p≥0 and RF be its left Martindale quotient ring. If ф(Xi^△j) is a reduced generalized differential identity for an essential ideal of R, then ф(Zije(△j )) is a generalized polynomial identity for RF, where e(△j) are idempotents in the extended centroid of R determined by △j. Let R be a prime ring and Q be its symmetric Martindale quotient ring. If ф(Xi△j) is a reduced generalized differential identity for a noncommutative Lie ideal of R, then ф(Zij) is a generalized polynomial identity for [R, R]. Moreover, if ф(Xi△j) is a reduced generalized differential identity, with coefficients in Q, for a large right ideal of R, then ф(Zij) is a generalized polynomial identity for Q.    

5.  The K_2-groups over Finaite Commutative Rings  
   南基洙  田子德《东北数学》,2002年第2期
   The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.    

6.  The K2-groups over Fimite Commutative Rings  
   南基洙  田子德《东北数学》,2002年第18卷第2期
   The present note determines the structure of the K2-group and of itssubgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 ≤ i ≤ m), where R ≌ m i=1 Ri and K2(R) ≌ m i=1 K2(Ri). We show that if charKi = p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.    

7.  ON EULER CHARACTERISTIC OF MODULES~(**)  
   佟文廷《数学年刊B辑(英文版)》,1989年第1期
   This paper gives a characteristic property of the Euler characteristic for IBN rings. The following results: are proved. (1) If R is a commutative ring, M, N are two stable free R-modules, then χ(MN)=χ(M)χ(N), where χ denotes the Euler characteristic. (2) If f: K_0(R)→Z is a ring isomorphism, where K_0(R) denotes the Grothendieck group of R, K_0(R) is a ring when R is commutative, then f([M])=χ(M) and χ(MN)=χ(M)χ(N) when M, N are finitely generated projective R-modules, where.the isomorphism class [M] is a generator of K_0(R). In addition, some applications of the results above are also obtained.    

8.  主理想环上子群Gr在线性群中的扩群  
   卫宗礼  曲贺梅《数学季刊》,2008年第23卷第4期
   Suppose R is a principal ideal ring,R~* is a multiplicative group which is composed of all reversible elements in R,and M_n(R),GL(n,R),SL(n,R) are denoted by, M_n(R)={A=(a_(ij))_(n×n)|a_(ij)∈R,i,j=1,2,…,n},GL(n,R) = {g|g∈M_n(R),detg∈R~*},SL(n,R) = {g∈GL(n,R)|det g=1},SL(n,R)≤G≤GL(n,R)(n≥3),respectively, then basing on these facts,this paper mainly focus on discussing all extended groups of G_r={(AB OD)∈G|A∈GL(r,R),(1≤r    

9.  The structure of a class of Z-local rings  
   WU Tongsuo & LU Dancheng Department of Mathematics  Shanghai Jiao Tong University  Shanghai 200240  China   Department of Mathematics  Suzhou University  Suzhou 215006  China《中国科学A辑(英文版)》,2006年第49卷第10期
   A local ring R is called Z-local if J(R) = Z(R) and J(R)2 = 0. In this paper the structure of a class of Z-local rings is determined.    

10.  J-clean and Strongly J-clean Rings  
   XIANG YUE-MING  OUYANG LUN-QUN《数学研究通讯:英文版》,2018年第3期
   Let R be a ring and J(R) the Jacobson radical. An element a of R is called(strongly) J-clean if there is an idempotent e ∈ R and w ∈ J(R) such that a = e + w(and ew = we). The ring R is called a(strongly) J-clean ring provided that every one of its elements is(strongly) J-clean. We discuss, in the present paper,some properties of J-clean rings and strongly J-clean rings. Moreover, we investigate J-cleanness and strongly J-cleanness of generalized matrix rings. Some known results are also extended.    

11.  斜Armendariz矩阵环  
   杨刚  刘仲奎  王彦军《数学研究与评论》,2010年第30卷第6期
   Let R be a ring.We show in the paper that the subring Un(R) of the upper triangular matrix ring Tn(R) is α-skew Armendariz if and only if R is α-rigid,also it is maximal in some non α-skew Armendariz rings,where α is a ring endomorphism of R with α(1) = 1.    

12.  Noetherian Skew Group Rings of F.C Groups  
   HU Chang-liu  WANG Jian-ping 《数学季刊》,2006年第21卷第3期
   Let R *θG be the skew group ring with a F.C group G and the group homom-rphismθfrom G to Aut(R), the group of automorphisms of the ring R. In this paper,the necessary and sufficient condition such that R*θG will be Noetherian is given, which generalizes the results of I.G. connel.    

13.  Semi Group Rings Which are Chinese Ring  
   W.B.Vasantha Kandasamy《数学研究与评论》,1993年第3期
   In this paper we obtain conditions under which a semigroup ring is a Chinese ring.Further we define what are called weakly Chinese rings and study them.The authors in[1]called a commutative ring R to be a Chinese ring if,given elements a,b∈R and idealI,J(?)R such that a≡b(I J)there exists an element c∈R such that c≡a(I)andc≡b(J).For more properties about Chinese rings please refer[1].    

14.  一个四元数矩阵方程的可解性  被引次数:3
   曹文胜《高校应用数学学报(英文版)》,2002年第17卷第4期
   § 1  IntroductionL et R be the real number field,C=R Ri be the complex numberfield,and H=C Cj=R Ri Rj Rk be the quaternion division ring over R,where k:=ij=- ji,i2 =j2 =k2 =- 1 .Ifα=a1 +a2 i+a3 j+a4 k∈ H ,where ai∈ R,then letα=a1 - a2 i- a3 j- a4 k bethe conjugate ofα.L et Hm× nbe the setof all m× n matrices over H.If A=(aij)∈ Hn× n ,L etATbe the transpose matrix of A,A be the conjugate matrix of A,and A* =(aij) T be thetranspose conjugate matrix of A.A∈Hn× nis said…    

15.  Existence Results for Nonlinear Subelliptic Equations on the Heisenberg Group  
   罗学波  张吉慧《东北数学》,1999年第4期
   § 1.Introduction  The aim of this paper is to establish existence results,by monotone method,for theproblemΔHnu + f((z,t) ,u) =0   in D,u| D =0 (1 .1 )where D is an open subset of the Heisenberg group HnandΔHn is the subelliptic Lapla-cian on Hn.We recall that Hnis the Lie group whose underlying manifold is Cn× R,n∈N,endowed with the group law(z,t) (z′,t′) =(z + z′,t+ t′+ 2 Imz .z′) ,(1 .2 )where for z,z′∈ Cnwe have letz .z′= nj=1zjz′j.Set zj=xj+ iyj.Then (x1 ,… ,xn…    

16.  K─f环的张量积  
   周伟《数学研究与评论》,1994年第14卷第1期
   A multiplication is introduced into the tensor products of K一lattice ordered modules、where K is a commutative lottice ordered ring with identity.It is shown that the positivecone of the Abelian l-group of the tensor products is closed under this multiplication andthat the tensor products of K-f rings is a K-lattice ordered ring.    

17.  Maximal Quotient Rings of Endomorphisms of Quasigenerators  
   朱胜林《数学研究与评论》,1989年第2期
   O.Preliminaries. Let R be an associative ring with identity, and let Mod-R denote the category of all unital right R-modules. A set of right ideal of R is called a Gabriel topology on R if satisfies T1. If I∈ and I J, then J∈. T2. If I and J belong to, then I∩J∈. T3. I∈ and r∈R, then (I:r)={x∈R:rx∈I}∈. T4. If I is a right ideal of R and there exists J∈ such that (I:r)∈ for every r∈J, then I∈.    

18.  COINDUCED REPRESENTATIONS AND INJECTIVE MODULES FOR HYPERALGEBRA b_r  
   王建磐《数学年刊B辑(英文版)》,1983年第3期
   Let G be a simply connected semisimple linear algebraic group over an algebraicallyclosed field of positive characteristic p,B its Borel subgroup,and b_r the r-th standard subal-gebra of the hyperalgebra of B.Assume the roots in B to be negative.Using the coinduced representations,in this paper the author proves:(1)J(r,λ)=St_r((p~r-1)δ+λ)is the b_r-injective envelope of the one-dimensionalb_r-module λ,where St_r is the r-th Steinberg module of G,and δ half the sum of the positiveroots.(2)With respect to the natural homomorphism p_(rs):J(r,λ)→J(s,λ)(r≤s),J(∞,λ)=lim J(r,λ)is the B-injective envelope of B-module λ.The above conclusions positively answer two questions posed by J.E.Humphreys atShanghai in 1980.Moreover,this paper gives a complete description of injective b_r-modules.    

19.  弱对偶环  
   魏俊潮  孙建华《东北数学》,2004年第20卷第4期
   In This paper, the concept of weakly dual ring is introduced, which is a proper generalization of the dual ring. If R is a right weakly dual ring, then (1) Z(RR) = J(R); (2) If R is also a zero-division power ring, then R is a right AP-injective ring. In addition, some properties of weakly dual rings are given.    

20.  On Skew Triangular Matrix Rings  
   《数学研究通讯:英文版》,2016年第3期
   Letαbe a nonzero endomorphism of a ring R, n be a positive integer and Tn(R,α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by Tn(R,α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x;α]/(xn), where R[x;α] is the skew polynomial ring.    

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