共查询到20条相似文献,搜索用时 680 毫秒
1.
张跃辉 《中国科学A辑(英文版)》2002,45(6):741-748
Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra
T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the
maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of
A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if
and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the
exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there
exists an idempotent e of A, and an invertible element u of A, such that eBe = u-1eCeu. 相似文献
2.
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
3.
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
4.
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
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
5.
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
6.
A linear mapping φ from an algebra A into its bimodule M is called a centralizable mapping at G ∈ A if φ(AB)=φ(A)B=Aφ(B) for each A and B in A with AB=G. In this paper, we prove that if M is a von Neumann algebra without direct summands of type I1 and type II, A is a *-subalgebra with M ⊆ A ⊆ LS(M) and G is a fixed element in A, then every continuous (with respect to the local measure topology t(M)) centralizable mapping at G from A into M is a centralizer. 相似文献
7.
设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定.本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数. 相似文献
8.
本文给出了算子方程AXB-X=C可解的若干充要条件,其中(A,B)为下列情形之一:A或B有闭值域;A(B*)有闭值域并且是单射或者相似于一个协亚正规算子并且B(A*)是单侧移位;A+(B(*+))幂有界,其值域R(A+) R(A)(R(B) R(B+)并且B(A*)是单侧移位;A=U*且B=U是Hardy空间上重数为1的单侧移位.而且,给出了解的表达式. 相似文献
9.
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
10.
对于任意的n阶实矩阵A,给出了A(A*)T与A的奇异性间的关系,指出了A(A*)T的行和与列和为矩阵A的行列式|A|,最后给出了矩阵类A(A*)T与n阶方阵的一个等价类的一一对应关系. 相似文献
11.
讨论了分次环A,Ae和A#G*的相关性质,在A是分次忠实时,A#G*是亚直既约环当且仅当Ae是亚直既约环;在A是分次非退化时,A#G*是G亚直既约环当且仅当A是分次亚直既约环. 相似文献
12.
The concept of Koszul differential graded (DG for short) algebra is introduced in [8]. Let A be a Koszul DG algebra. If the Ext-algebra of A is finite-dimensional, i.e., the trivial module Ak is a compact object in the derived category of DG A-modules, then it is shown in [8] that A has many nice properties. However, if the Ext-algebra is infinite-dimensional, little is known about A. As shown in [15] (see also Proposition 2.2), Ak is not compact if H(A) is finite-dimensional. In this paper, it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality. A DG version of the BGG correspondence is deduced from the Koszul duality theorem. 相似文献
13.
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
14.
15.
设WMμ为系统MIPC*全部公式的集,再设г∪{A} WMμ,则гMIPC* A意义明显.而 M A指гM-蕴涵A.以前已证明гM A гMIPC*A,即MIPC*为强完全的.本文证明其逆定理成立,即гMIPC*A гM A.是为MIPC*的可靠性定理. 相似文献
16.
张欣 《数学的实践与认识》2007,37(10):173-177
讨论了一类模糊双向联想记忆网络极限环的最大长度.首先,A是强连通布尔矩阵时,极限环的最大长度是A的周期指数per(A);其次,A具有形式(☆)时,若gcd(per(A1),per(A2))=1,则极限环的最大长度为max(per(A1),per(A2));若gcd(per(A1),per(A2))≥2,则其最大长度为lcm(per(A1),per(A2));最后对其进行推广. 相似文献
17.
A class of A-modules is socle-fine if for any A-modules M and N in this class, M and N are isomorphic if and only if socle of M and socle of N are isomorphic. A ring A is a left V-ring if and only if the class of indecomposable quasi-injective A-modules with large socle is socle-fine. A ring A is a left V-ring noetherian if and only if the class of quasi-injective /4-modules with large socle is socle-fine. A ring A is Pseudo-Frobenius if and only if A is a left, cogenerator and the class of projective A-modules is socle-fine. 相似文献
18.
本文证明了下列结果:(i)四元数矩阵A可写成两个自共轭四元数矩阵的乘积A相似于实矩阵A Hermite相似于A~*.(ii)A可写成一个半正定自共轭四元数矩阵与一个自共轭四元数矩阵的乘积A相似于实对角矩阵或者A~diag(D,I_r(×)J_2(O)),其中D是一个实对角矩阵.本文还给出了体上实矩阵AB与BA相似的一个充要条件. 相似文献
19.
Jerzy Matczuk 《代数通讯》2013,41(3):725-746
Let a monoid S act on a ring R by injective endomorphisms and A(R; S) denote the S-Cohn–Jordan extension of R. A series of results relating properties of R and that of A(R; S) are presented. In particular it is shown that: (1) A(R; S) is semiprime (prime) iff R is semiprime (prime), provided R is left Noetherian; (2) if R is a semiprime left Goldie ring, then so is A(R; S), Q(A(R; S)) = A(Q(R); S) and udim R = udim A; (3) A(R; S) is semisimple iff R is semisimple, provided R is left Artinian. Some applications to the skew semigroup ring R#S are given. 相似文献
20.
本文给出了一个关联图为圈的非负、半正定矩阵A为完全正的一个充要条件.我们还证明了这样的矩阵A(当A为完全正时)的分解指数即为A的阶数. 相似文献