Gorenstein代数上的Hopf代数作用

令H是有限维Hopf代数，A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广，同时给出A/A^H是Frobenius扩张的条件。     

有消费或投资的华氏宏观经济模型

本文对华罗庚教授的宏观经济模型进行了推广 ,在原来模型的基础上 ,分别增加了消费、投资 ,得到两种不同的模型 ,并对模型具有经济意义的解进行了研究     

The dual of a constacyclic code,self dual,reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3

Over finite local Frobenius non-chain rings with nilpotency index 3 and when the length of the codes is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of $\gamma$-constacyclic codes is established and the algebraic characterization of self-dual $\gamma$-constacyclic codes, reversible $\gamma$-constacyclic codes and $\gamma$-constacyclic codes with complementary dual are given. Generators for the dual code are obtained from those of the original constacyclic code.     

Associated Primes of the Example of Brenner and Monsky

Recently, Brenner and Monsky found an example of an ideal in a hypersurface ring whose tight closure does not commute with localization, thus answered the localization problem in tight closure theory in the negative. In this article, we use Monsky's calculations to analyze the set of associated primes of the Frobenius powers of this ideal and show that this set is infinite.     

Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.

     

Frobenius problem for semigroups \mathsf{S}(d_{1},d_{2},d_{3})

We find the matrix representation of the set Δ(d ³), where d ³=(d ₁,d ₂,d ₃), of integers that are unrepresentable by d ₁,d ₂,d ₃ and develop a diagrammatic procedure for calculating the generating function Φ(d ³;z) for the set Δ(d ³). We find the Frobenius number F(d ³), the genus G(d ³), and the Hilbert series H(d ³;z) of a graded subring for nonsymmetric and symmetric semigroups and enhance the lower bounds of F(d ³) for symmetric and nonsymmetric semigroups.      

四元数矩阵方程AX-YB=C的最佳逼近解

本利用四元数矩阵的广义Frobenius范数建立一个关于四元数矩阵的实函数，并讨论了它的极值问题．然后在四元数矩阵方程AX-YB=C的解集合中导出了与给定矩阵的最佳逼近解的表达式．     

谱约束下对称正交对称矩阵束的最佳逼近

讨论了对称正交对称矩阵的广义逆特征值问题，得到了通解表达式和最佳解的表达式。     

Cluster Categories Coming from Cyclic Posets

Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14 Igusa , K. , Todorov , G. ( 2013 ). Continuous Frobenius categories . Proceedings of the Abel Symposium 2011 : 115 – 143 .[Crossref] , [Google Scholar]], the infinity-gon of [12 Holm , T. , Jøot rgensen , P. ( 2012 ). On a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon . Math. Z. 270 : 277 – 295 .[Crossref], [Web of Science ®] , [Google Scholar]], and the m-cluster category of type A _∞ (m ≥ 3) [13 Holm , T. , Jøot rgensen , P. ( 2015 ). Cluster tilting vs. weak cluster tilting in Dynkin type A infinity . Forum Math. 27 : 1117 – 1137 .[Crossref], [Web of Science ®] , [Google Scholar]] are examples of this construction as well as some new examples such as the cluster category of ?². An extension of this construction and further examples are given in [16 Igusa, K., Todorov, G. Continuous Cluster Categories of Type D. arXiv:1309.7409 . [Google Scholar]].