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1.
A complex matrix A is said to be a matrix realization of the digraph D if D is the associated digraph of A, and A is said to have the property B if every singular value of A is contained in the union of Brualdi-type intervals. A digraph D is said to be a forcible B-digraph if every matrix realization of D has the property B. In this paper, we give a sufficient condition for a matrix to have the property B and characterize the forcible B-digraphs.  相似文献   

2.
Let A be a monomial quasi-hereditary algebra with a pure strong exact Borel subalgebra B.It is proved that the category of induced good modules over B is contained in the category of good modules over A;that the characteristic module of A is an induced module of that of B via the exact functor-(?)_B A if and only if the induced A-module of an injective B-module remains injective as a B-module.Moreover,it is shown that an exact Borel subalgebra of a basic quasi-hereditary serial algebra is right serial and that the characteristic module of a basic quasi-hereditary serial algebra is exactly the induced module of that of its exact Borel subalgebra.  相似文献   

3.
From the area of a square you can determine the length ofany of its sides.If the length of the side is √A.That is why√A is called the square root of A. Just as a plant rests on itsroots,a square can rest on its(positive)square root.side=√AThus if the area of a square is 400 square feet,its side has length 20cm.If the area is 13square feet,its side has length √13 feet,You can verify the latter of these with a calculator:  相似文献   

4.
In this paper.we study the ring #(D.B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B.D)-Hopf modules BM^D.Cai and Chen have proved this result in the case B=D=A.Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A).We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A.A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral.Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A).Moreover we prove that the left singular ideal of the ring #(A,A)is zero.A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension.  相似文献   

5.
A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A bounded semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of zero divisors and prime elements of a bounded semiring are studied. In particular, it is proved that under some mild assumption, the set Z(A) of nonzero zero divisors of A is A / {0, 1}, and each prime element of A is a maximal element. For a bounded semiring A with Z(A) = A / {0, 1}, it is proved that A has finitely many maximal elements if ACC holds either for elements of A or for principal annihilating ideals of A. As an application of prime elements, we show that the structure of a bounded semiring A is completely determined by the structure of integral bounded semirings if either |Z(A)| = 1 or |Z(A)| -- 2 and Z(A)2 ≠ 0. Applications to the ideal structure of commutative rings are also considered. In particular, when R has a finite number of ideals, it is shown that the chain complex of the poset I(R) is pure and shellable, where I(R) consists of all ideals of R.  相似文献   

6.
Let k be the algebraic closure of a finite field F_q and A be a finite dimensional k-algebra with a Frobenius morphism F.In the present paper we establish a relation between the stable module category of the repetitive algebra  of A and that of the repetitive algebra of the fixed-point algebra A~F.As an application,it is shown that the derived category of A~F is equivalent to the subcategory of F-stable objects in the derived category of A when A has a finite global dimension.  相似文献   

7.
A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Links of the same feature have the same cost. It is proved that the problem of finding ?routing tree of the minimum cost for a given set of tasks of two features is NP-complete.  相似文献   

8.
<正> We shall extend the concepts of the kernel and the image of the homomorphism φ in Abstract Algebra to the bounded linear operator of L_p space. We can obtain some results. Definition 1 let A be a L_p space, B(?)A. If B is a L_p space by the operation and the norm in A, then the subset B of A is called a L_p subspace of A.  相似文献   

9.
Recently, Markham has proved the following property of M-matrices. Theorem A Suppose A is an M-matrix with the property that for some positive integer p, A~p=L, where L is a lower-triangular matrix. Then A is a lower-triangular matrix. Clearly Theorem A is also true for an upper-triangular matrix. The purpose of this note is to generalize Theorem A to a block upper triangular matrix. If A is a real square matrix with nonpositive off-diagonal elements, each of the following is a necessary and sufficient condition for A to be an M-matrix.  相似文献   

10.
This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given.  相似文献   

11.
詹建明  谭志松 《东北数学》2004,20(2):145-152
In this paper, we introduce the concept of T-local derivations and obtain the main result: each T-local derivation of avon Neumann algebra A into a dual A-bimodule M is a T-derivation, where T is an endomorphism of A to A.  相似文献   

12.
Let A be a three-point algebra with Gabriel quiver the system quiver Q, Then, up to isomorphism and duality, A is tame if and only if A is or degenerates to a factor of a tame algebra in the tame Table T if and only if A/rad5 A is tame, and A is wild if and only if A has a wild algebra in the wild Table W as a factor if and only if A is controlled wild.  相似文献   

13.
如果 A是 Hilbert 空间上的完全分配格代数,  那么A中秩一算子生成的子代数在 A中弱稠密, 当且仅当,A在迹尖算子空间中的一次和二次预零化子的弱闭包是自反的;如果A是套代数,那么LatA是极大套,当且仅当,A的包含A-的每个弱闭子空间是自反的,其中  相似文献   

14.
Fillmore在[1]中得到一个定理:设A,T是Banach空间X上的线性变换,A有界,若Lat(A) Lat(T)且AT=TA,则T是A的多项式.在本文里,以此作为引理,讨论了Banach空间上可逆线性变换A在什么情况下,A-1可表示为A的多项式.本文最主要的结论是定理3.4:设X是Banach空间,A是X上的有界线性变换,且可逆,则A-1是A的多项式当且仅当A-1是A的局部多项式.  相似文献   

15.
讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核,以及在什么情况下为绝对收缩核。  相似文献   

16.
曾广兴 《数学学报》1998,41(1):103-106
在本文中,严实Hilbert环得到了更进一步的刻划.本文的主要结果是:一个环A是严实Hilbert环,当且仅当多项式环A[X]的每个实极大理想在A上的局限是A的一个极大理想,当且仅当A是实Hilbert环,且A[X]的每个实极大理想是极大的.  相似文献   

17.
代数A在子代数A^H上投射的若干充分条件   总被引:1,自引:0,他引:1  
祝家贵 《数学杂志》1999,19(3):349-353
假设H是域k上的有限维Hopf代数,A是H-模代数,本文刻画了A^HA的投射性并给出了A^HA是投射的若干充分条件,其中A^H是A的H-不变子代数。  相似文献   

18.
纪培胜  王琳 《数学学报》2004,47(5):867-872
本文给出了GICAR代数中闭Lie理想的完全刻画.设A是GICAR代数,L是A的闭Lie理想,则存在A的闭理想J,使得[A,J]=[J,J](?) L (?) π-1(Z(A/J)),其中π是A到A/J上的商映射.反之,任意这种形式的闭子空间L是A的闭Lie理想.  相似文献   

19.
阮颖彬  严子锟 《数学学报》2000,43(2):343-348
本文证明了每一个p-亚正常算子A,都相应存在一个亚正常算子 ,使得A与 有相同的闭值域点、相同的本质谱和谱.由此推出如果A是p-亚正常算子,B是任一有界线性算子,若存在有界线性算子X有稠值域,使得XB=AX,则σ(A)(B)此外还证明了,如果A是p-亚正常算子且 R(A)闭或KerA=KerA*, B是任一有界线性算子,A与B拟相似,则e(A)(B).  相似文献   

20.
毛雪峰  谢建峰 《数学学报》2018,61(5):715-728
本文给出了有关同调光滑连通上链微分分次(简称DG)代数的两个重要结论.具体地说,当A是同调光滑连通上链DG代数且其同调分次代数H(A)是诺特分次代数时,证明D_(fg)(A)中的任意Koszul DG A-模都是紧致的.另外,当A是Kozul连通上链DG代数且其同调分次代数H(A)是有平衡对偶复形的诺特分次代数时,证明A的同调光滑性质等价于D_(fg)(A)=D~c(A).  相似文献   

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