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共有20条相似文献,以下是第1-20项 搜索用时 109 毫秒

1.  Maximal subalgebras of the general linear Lie algebra containing Cartan subalgebras  
   DengYin Wang  Hui Ge  XiaoWei Li《中国科学 数学(英文版)》,2012年第55卷第7期
   Let gln(R) be the general linear Lie algebra of all n × n matrices over a unital commutative ring R with 2 invertible, dn(R) be the Cartan subalgebra of gln(R) of all diagonal matrices. The maximal subalgebras of gln(R) that contain dn(R) are classified completely.    

2.  关于w-linked扩环  被引次数:1
   谢林  王芳贵  田艳《数学研究与评论》,2011年第31卷第2期
   Let R ■ T be an extension of commutative rings.T is called w-linked over R if T as an R-module is a w-module.In the case of R ■ T ■ Q 0 (R),T is called a w-linked overring of R.As a generalization of Wang-McCsland-Park-Chang Theorem,we show that if R is a reduced ring,then R is a w-Noetherian ring with w-dim(R) 1 if and only if each w-linked overring T of R is a w-Noetherian ring with w-dim(T ) 1.In particular,R is a w-Noetherian ring with w-dim(R) = 0 if and only if R is an Artinian ring.    

3.  强P除环上方阵的酉相似理论(Ⅱ)  被引次数:11
   屠伯埙《数学研究与评论》,1988年第8卷第1期
   This is a continuation of the previous paper ( 1 ) . In this paper , a useful basic theorem that every selfconjugate matrix over the strong p division ring Ω is unitary similar to a tridiagorial matrix over the conter of Ω is given thus all of famous results involving selfconjugate matrices, positivedefinite selfcon jugate matrices, nonnegative selfconjugate matrix in the ordiniry com plex matrix theory are generalized to selfconjugate matrices over Ω . and Sigular decomuposition as well as polar decomposition in the ordinary complex matrix theory are also generalized to matrices over Ω .    

4.  Zip模(英文)  
   张翠萍  陈建龙《东北数学》,2008年第24卷第3期
   A ring R is called right zip provided that if the annihilator τR(X) of a subset X of R is zero, then τR(Y) = 0 for some finite subset Y C X. Such rings have been studied in literature. For a right R-module M, we introduce the notion of a zip module, which is a generalization of the right zip ring. A number of properties of this sort of modules are established, and the equivalent conditions of the right zip ring R are given. Moreover, the zip properties of matrices and polynomials over a module M are studied.    

5.  Generalized PP and Zip Subrings of Matrix Rings  
   LIU ZHONG-KUI  QIAO HU-SHENG《东北数学》,2010年第26卷第3期
   Let R be an abelian ring. We consider a special subring An, relative to α2,…, αn∈ REnd(R), of the matrix ring Mn(R) over a ring R. It is shown that the ring An is a generalized right PP-ring (right zip ring) if and only if the ring R is a generalized right PP-ring (right zip ring). Our results yield more examples of generalized right PP-rings and right ziu rings.    

6.  A CHARACTERIZATION OF THE GENERALIZED INVERSES OVER DIVISION RINGS  
   《高等学校计算数学学报(英文版)》,2000年第Z1期
   Peal[2] shows that a sufficient and necessary condition on the existence of theMoore-Penrose inverse over any fields.Zhuang [3] generalize the result to any divisionrings.In this section we give another sufficient and necessary condition on the existence ofthe Moore-Penrose inverse over any division rings.Our result can be regarded as an im-provement of Theorem lin[1].As a medium result,we also show a characterization ofthe{1,2}-inverse.    

7.  OPERATOR AND MATRIX REPRESENTATION FOR THE GENERALIZED INVERSE A_(T,S)~(2)  
   陈永林《应用数学学报(英文版)》,2001年第1期
   . IntroductionIn this paper we adopt the same notations on generalized inverses of matrices andprojectors as those in [1].Several rePresentations for the generalized inverses of matrices, for example, those forthe Moors-Penrose inverse A and the Drazin inverse A(d), have led to[1--4]:where k = index (A).In order to study the matrix form of the above-mentioned operator represelltations,we denote linear operators by A, B,' ', and their matrices by the corresponding A, B,' '.All of the li…    

8.  H-separable Hopf Galois Extensions and Azumaya Algebra  
   祝家贵《东北数学》,2001年第3期
   1 IntroductionLet A/R be a ring extension with the common identity 1. A/R is said to be separable if theA-bimodule homomorphism of A @R A onto A defined by a @ 5-a6 splits. A separableextension over a non-commutative ring generalizes that over a commutative ring which wasdiscussed in [1]. Hirata introduced anOther kind of separable extensions called H-separabeones (see [2]). A/R is said to be H-separable if A @R A is isomorphic as an A-bimoduleto a direct sumrnand of A". riom {2, Theor…    

9.  RESEARCH ANNOUNCEMENTS A Generalization if Goldie's Theorem  
   罗运伦《数学进展》,1986年第4期
   In this paper we proved two theorems which are generalizations of Goldie’sTheorem, Definition 1.A ring R is said to be a right G-ring,if R satisfies (i)For any nonezero left ideal L of R,there exists 0≠x∈L,for any S,t∈R, st≠0,xt≠0 imply sxt≠0. (ii)For any x∈R,the right Goldie’s dimension of xR is finite. Definition 2.Let Δ be a division ring and N be a veetor space over Δ,a    

10.  A CONJECTURE CONCERNING THE HADAMARD PRODUCT OF INVERSE M-MATRICES  
   《高等学校计算数学学报(英文版)》,2000年第Z1期
   1 IntroductionFor an n×n matrix A which is an inverse M-matrix,M.Neumann in [1]conjecturedthat the Hadamard product A·A is an inverse of an M-matrix.They have checked hisconjecture without failure on Ultrametric matrices and inverse of MMA-matrices,Uni-pathicmatrices and the Willongby inverse M-matrices.Bo-Ying Wang et al.in[2]haveinvestigated Triangular inverse M-matrices which are closed under the Hadamard multipli-cation.Lu Linzheng,Sun Weiwei and Li Wen in[3]presented a more general conjecture    

11.  On Maximal Injectivity  被引次数:4
   Ming Yi WANG Guo ZHAO《数学学报(英文版)》,2005年第21卷第6期
   A right R-module E over a ring R is said to be maximally injective in case for any maximal right ideal m of R, every R-homomorphism f : m → E can be extended to an R-homomorphism f^1 : R → E. In this paper, we first construct an example to show that maximal injectivity is a proper generalization of injectivity. Then we prove that any right R-module over a left perfect ring R is maximally injective if and only if it is injective. We also give a partial affirmative answer to Faith's conjecture by further investigating the property of maximally injective rings. Finally, we get an approximation to Faith's conjecture, which asserts that every injective right R-module over any left perfect right self-injective ring R is the injective hull of a projective submodule.    

12.  Additive preservers of idempotence and Jordan homorphisms between rings of square matrices  
   Hong Mei Yao   Chong Guang Cao and Xian Zhang《数学学报(英文版)》,2009年第25卷第4期
   Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n x n matrices over R. Let (Jn(R)) be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let JJ = (Jn(R)) or Mn(R). We describe the additive preservers of idempotence from JJ to Mm(R) when 2 is a unit of R. Thereby, we also characterize the Jordan (respectively, ring and ring anti-) homomorphisms from Mn (R) to Mm (R) when 2 is a unit of R.    

13.  GEOMETRY OF RECTANGULAR MATRICES OVER A SIMPLE ARTINIAN RING  
   《高等学校计算数学学报(英文版)》,2000年第Z1期
   Let R be a simple Artinian ring,M_(m×n)(R) be the set of all m×n matrices over R.GL_n(R) be the set of all n×n invertible matrices over R.Let A~T be the transpose matrix ofA∈M_(m×n)(R).By the Wedderburn-Artin theorem,R be isomorphic to a total matrix ringM_(s×s)(D) over a division ring D.Let α→(α)_D be an isomorphism of R onto M_(s×s)(D), if X=    

14.  Geometry of 2×2 hermitian matrices  被引次数:2
   黄礼平  万哲先《中国科学A辑(英文版)》,2002年第45卷第8期
   Let D be a division ring which possesses an involution a→ā. Assume that F = {a∈D|a=ā} is a proper subfield of D and is contained in the center of D. It is pointed out that if D is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two, D is a separable quadratic extension of F. Thus the trace map Tr: D→F,hermitian matrices over D when n≥3 and now can be deleted. When D is a field, the fundamental theorem of 2×2 hermitian matrices over D has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two.    

15.  交换环上上三角矩阵的李三导子  
   李海玲  王颖《数学研究与评论》,2010年第30卷第3期
   Let T(n, R) be the Lie algebra consisting of all n× n upper triangular matrices over a commutative ring R with identity 1 and M be a 2-torsion free unital T(n, R)-bimodule. In this paper, we prove that every Lie triple derivation d : T(n, R) →M is the sum of a Jordan derivation and a central Lie triple derivation.    

16.  主理想整环上n阶矩阵环中的Goldbach问题  
   胡维《东北数学》,2005年第3期
   Abstract: In this paper, we consider the Goldbach's problem for matrix rings, namely, we decompose an n ×n (n > 1) matrix over a principal ideal domain R into a sum of two matrices in Mn(R) with given determinants. We prove the following result: Let n > 1 be a natural number and A = (αij) be a matrix in Mn(R). Define d(A) := g.c.d{αij}. Suppose that p and q are two elements in R. Then (1) If n > 1 is even, then A can be written as a sum of two matrices X, Y in Mn(R) with det(X) = p and det(Y) = q if and only if d(A) |p-q; (2) If n > 1 is odd, then A can be written as a sum of two matrices X, Y in Mn(R) with det(X) = p and det(Y) = q if and only if d(A) |p + q. We apply the result to the matrices in Mn(Z) and Mn(Q[x]) and prove that if R = Z or Q[x], then any nonzero matrix A in Mn(R) can be written as a sum of two matrices in Mn(R) with prime determinants.    

17.  Modular Automorphisms of Upper Triangular Matrices over a Commutative Ring Preserving Rank One  被引次数:1
   Cao Chongguang《东北数学》,1994年第4期
   Modular Automorphisms of Upper Triangular Matrices over a Commutative Ring Preserving Rank OneCaoChongguang(曹重光)(Departmentof...    

18.  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…    

19.  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.    

20.  Comparability for ideals of regular rings  
   CHEN Huanyin Department of Mathematics  Zhejiang Normal University  Jinhua 321004  China《中国科学A辑(英文版)》,2005年第48卷第6期
   In this paper we investigate necessary and sufficient conditions under which the ideals possess comparability structure. For regular rings, we prove that every square matrix over ideals satisfying general comparability admits a diagonal reduction by quasi-invertible matrices.    

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