Journal of Guangxi Normal University(Natural Science Edition) ›› 2015, Vol. 33 ›› Issue (1): 74-79.doi: 10.16088/j.issn.1001-6600.2015.01.012

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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

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

CLC Number: 

  • O175
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