期刊信息
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- 刊名: 河北师范大学学报(自然科学版)Journal of Hebei Normal University (Natural Science)
- 主办: 河北师范大学
- ISSN: 1000-5854
- CN: 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
一阶Weyl代数A1模k(x)的子模分类
-
1. 南京师范大学 泰州学院, 江苏 泰州 225300;
2. 扬州大学 数学科学学院, 江苏 扬州 225002 -
DOI:
10.11826/j.issn.1000-5854.2014.01.001
Classification of the Submodules of k(x) over the First Weyl Algebra A1
摘要/Abstract
摘要:
通过对一元多项式环k[x]上所有乘法子集进行分类,给出了一阶Weyl代数A1上模k(x)的所有非零子模的分类.
Abstract:
In this paper, all the nonzero submodules of k(x) over the first Weyl algebra A1 are classified by the classification of the multiplicative subsets of the polynomial ring k[x].
关键词
Key words:
Weyl algebra
;
localization
;
multiplicative subset
参考文献 12
- [1] OAKU T,TAKAYAMA N.Algorithms for D-modules-restriction,Tensor Product,Localization,and Local Cohomology Groups [J].J Pure Appl Algebra,2001,156(2/3):267-308.
- [2] TSAI H,WALTHER U.Computing Homomorphisms Between Holonomic D-modules [J].J Symbolic Comput,2001,32(6):597-617.
- [3] OAKU T,TAKAYAMA N,TSAI H.Polynomial and Rational Solutions of Holonomic Systems [J].J Pure Appl Algebra,2001,164(1/2):199-220.
- [4] 李会师.Weyl代数研究简介 [J].数学进展,1998,27(2):103-121.
- [5] WANG Zhihua,WEI Junchao,LI Libin.Poincare Series and an Application to Weyl Algebras [J].Acta Math Scientia,2011,31B(2):459-467.
- [6] LEYKIN A.Constructibility of the Set of Polynomials with a Fixed Bernstein-Sato Polynomial:An Algorithmic Approach [J].J Symbolic Comput,2001,32(6):663-675.
- [7] WALTHER U.Bernstein-Sato Polynomials Versus Cohomology of the Milnor Fiber for Generic Hyperplane Arrangements [J].Compositio Math,2005,141(1):121-145.
- [8] KASHIWARA M.On the Holonomic Systems of Linear Differential Equations II [J].Invent Math,1978,49(2):121-135.
- [9] COUTINHO S C.A Primer of Algebraic D-modules [M].Cambridge:Cambridge University Press,1995:171-178.
- [10] BLOCK R E.The Irreducible Representations of the Lie Algebrasl(2) and of the Weyl Algebra [J].Adv Math,1981,39:69-110.
- [11] WANG Zhihua,LI Libin.On Holonomic Module k [J].J Math,2013,33(5):773-780.
- [12] SERGE L.Algebra [M].New York:Springer-verlag,2002:573-574.