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1.
The author introduces twist vectors of control nets of parametric triangular Bèziersurfaces.With twist vectors and other geometric magnitudes,a sufficient condition forparametric triangular Bèzier surfaces to be convex is offered.Incidently,a necessary andsufficient condition for triangular Bèzier surfaces of parametric form to degenerate to thatof functional form is given.A less stringent sufficient condition is proposed for quadraticBèzier surfaces to be convex.  相似文献   

2.
In this paper, firstly, a necessary condition and a sufficient condition for an isomorphism between two semiring-induced valuation algebras to exist are presented respectively. Then a general valuation homomorphism based on different domains is defined, and the corresponding homomorphism theorem of valuation algebra is proved.  相似文献   

3.
Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod(R). As an application, it is proved that the "Minimal Horseshoe Lemma" is true in the category of quasi-d-Koszul modules under certain conditions.  相似文献   

4.
In this paper, we first give a sufficient and necessary condition for a Hopf algebra to be a Yetter-Drinfel'd module, and prove that the finite dual of a Yetter-Drinfel'd module is still a Yetter-Drinfel'd module. Finally, we introduce a concept of convolution module.  相似文献   

5.
In this paper,we first give a sufficent and necessary condition for a Hopf algebra to be a Yetter-Drinfel‘d module,and prove that the finite dual of a Yetter-Drinfel‘d module is still a Yetter-Drinfel‘d module,Finally,we introduce a concept of convolution module.  相似文献   

6.
In this paper we construct a new quantum group Uq(osp(1,2,f)),which can be seen as a generalization of Uq(osp(1,2)).A necessary and sufficient condition for the algebra Uq(osp(1,2,f)) to be a super Hopf algebra is obtained and the center Z(Uq(osp(1,2,f))) is given.  相似文献   

7.
In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke's Theorem for (H, B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B.  相似文献   

8.
We construct a class of modules for extended affne Lie algebra ■ by using the free fields. A necessary and sufficient condition is given for those modules being irreducible.  相似文献   

9.
卢业广 《数学季刊》1994,9(1):106-110
In this paper,the Alprin‘s conjecture is verified for △- tilt algebras,where △ is not a wild quiver;and a necessary and sufficient condition for F(X)being resolving is also given,where X is an exceptional sequence over a hereditary algebra.  相似文献   

10.
王志玺  武艳辉 《东北数学》2004,20(4):403-410
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra, ln this paper, we characterize the projectivity (injectivity) of M as a left A#σ H-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σ H, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.  相似文献   

11.
In this paper, we introduce the concept of sub-strongly maximal triangular algebras which form a large class of maximal triangular algebras, and prove that every algebraic isomorphism of sub-strongly maximal triangular algebras is spatially implemented, which generalizes the result by Ringrose in two respects.

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12.
We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite-dimensional algebra to be quasi-hereditary is the existence of a full and divisible standard system. As a further application, we obtain a sufficient condition for a standardly stratified algebra.  相似文献   

13.
设m和n是任意固定的非零整数且(m+n)(m-n)≠0,u是一个|mn(m+n)|-无挠的三角代数,D={d_k}_(k∈N)是u上的一个(m,n)-高阶可导映射.本文证明了:三角代数u上的每一个(m,n)-高阶可导映射都是高阶导子.作为结论的应用,得到了套代数或|mn(m+n)|-无挠的上三角分块矩阵代数上的每一个(m,n)-高阶可导映射都是高阶导子.  相似文献   

14.
15.
Jordan isomorphisms of triangular rings   总被引:1,自引:0,他引:1  
We investigate Jordan isomorphisms of triangular rings and give a sufficient condition under which they are necessarily isomorphisms or anti-isomorphisms. As corollaries we obtain generalizations of two recent results: the one concerning Jordan isomorphisms of triangular matrix algebras by Beidar, Bresar and Chebotar, and the one concerning Jordan isomorphisms of nest algebras by Lu.

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16.
令H是半单弱Hopf代数, A是左H-模代数.我们证明了正则A-模的内射维数, A#H-模A的内射维数和正则A#H-模的内射维数三者是相等的. 而且,利用H在A上的不动点代数我们给出了A是Gorenstein代数的充要条件.  相似文献   

17.
In Tang and Bai [Math Nachr. 2012;285:922–935] classified a class of non-graded left-symmetric algebraic structures on the Witt algebra under a certain rational condition. In this note, we show that this rational condition is not necessary. This leads to a more elegant classification of the left-symmetric algebraic structures and Novikov algebraic structures on the Witt algebra.  相似文献   

18.
李鹏同  鲁世杰 《东北数学》2002,18(4):323-329
Let U be a weakly closed nest algebra module acting on a Hilbert space H. Given two operators X and Y in B(H), a necessary and sufficient condition for the existence of an operator T in U satisfying TX = Y is provided.  相似文献   

19.
二宽度CSL代数的直和分解   总被引:1,自引:1,他引:1  
本文给出了可分Hilbert空间上的二宽度CSL代数分解成其对角与它的一个范数闭理想(即满足Ringrose条件的算子集)直和的充要条件是:此二宽度CSL是由一个有限CSL与一个有补CSL生成的.  相似文献   

20.
Let 𝒜 and ? be unital algebras over a commutative ring ?, and ? be a (𝒜,??)-bimodule, which is faithful as a left 𝒜-module and also as a right ?-module. Let 𝒰?=?Tri(𝒜,??,??) be the triangular algebra and 𝒱 any algebra over ?. Assume that Φ?:?𝒰?→?𝒱 is a Lie multiplicative isomorphism, that is, Φ satisfies Φ(ST???TS)?=?Φ(S)Φ(T)???Φ(T)Φ(S) for all S, T?∈?𝒰. Then Φ(S?+?T)?=?Φ(S)?+?Φ(T)?+?Z S,T for all S, T?∈?𝒰, where Z S,T is an element in the centre 𝒵(𝒱) of 𝒱 depending on S and T.  相似文献   

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