广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (1): 74-79.doi: 10.16088/j.issn.1001-6600.2015.01.012

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K[x1,x2;x-11,x-12] 上的分次扩张

孟淑慧, 尹方虎, 谢光明   

  1. 广西师范大学数学与统计学院,广西桂林541004
  • 收稿日期:2014-09-25 出版日期:2015-03-15 发布日期:2018-09-17
  • 通讯作者: 谢光明(1971—),男,四川自贡人,广西师范大学教授,博士。E-mail:gmxie@mailbox.gxnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11161005);广西科学基金资助项目(0991020);广西教育厅面上项目(200807MS016); 广西自然科学基金资助项目(2010GXNSFA013118)

Graded Extentions of K[x1, x2; x-11,x-12]

MENG Shu-hui, YIN Fang-hu, XIE Guang-ming   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541004, China
  • Received:2014-09-25 Online:2015-03-15 Published:2018-09-17

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摘要： 设V是域K上的一个全赋值环,B1=⊕i∈ZAi,0Xi1,B2=⊕j∈ZA0,jXj2分别是K[x1,x-11],K[x2,x-12]上V的分次扩张,令A=⊕i,j∈ZAi,jXi1Xj2是K[x1,x2;x-11,x-12]的一个子集, 本文对K[x1,x2;x-11,x-12] 中V的分次扩张进行了刻画。对B1、B2的所有可能的情形,本文证明了A的存在性,并讨论了B1、B2在若干条件下,A的唯一性。

关键词: 分次扩张, 全赋值环, 罗朗多项式环

Abstract: Let V be a total valuation ring of a field K,B1=⊕i∈ZAi,0Xi1 and B2=⊕j∈Z A0,jXj2 be graded extentions of V in K[x1,x-11] and K[x2,x-12] respectively. Let A=⊕i,j∈Z Ai,jXi1Xj2 be a subset of K[x1, x2; x-11, x-12]. Graded extensions of V in K[x1, x2; x-11, x-12] is described in this paper. For all cases of B1 and B2, the existence of A is proved. Furthermore, A being determined by B1 and B2 uniquely is also discussed in this paper.

Key words: graded extention, total valuation ring, Laurent polynomial ring

中图分类号: 

  • O175
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