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单边单项式序下的SAGBI基 被引量：1

SAGBI bases under one-sided monomial orderings
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摘要 设K是一个域,R是具有SM-基B的一个K-代数,且是B上一个单边(即左或右)单项式序.那么关于交换多项式代数和非交换自由代数的子代数在双边单项式序下经典的SAGBI基理论可完整地推广到R的子代数上来.特别地,对于一类N-分次代数,存在计算有限n-截断SAGBI基的有效算法,并且第一次阐明了在单边单项式序下讨论SAGBI基理论的可行性. Let K be a field,R a K-algebra with an SM-basis B,and a one-sided（i.e.left or right） monomial ordering on B.Then the classical SAGBI basis theory（w.r.t.a two-sided monomial ordering） for subalgebras of commutative polynomial algebras and noncommutative free algebras can be completely generalized to subalgebras of R.In particular,finite n-truncated SAGBI bases can be computed by means of effective algorithm,for the first time clarify the feasibility of discussing SAGBI basis theory under one-sided monomial ordering.
作者 赵志琴
机构地区 中山大学新华学院经济与贸易系
出处 《纯粹数学与应用数学》 CSCD 2011年第6期770-777,共8页 Pure and Applied Mathematics
基金 国家自然科学基金(10971044)
关键词 SM-基 子代数 SAGBI基 齐次SAGBI基 SM-basis subalgebra SAGBI basis homogeneous SAGBI basis
分类号 O154.3 [理学—基础数学]
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参考文献10

  • 1Robbiano L, Sweedler M. Subalgebra bases[J]. Commutative Algebra, 1988,1430:61-87.
  • 2Kapur D, Madlener K. A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra[C]. New York: Computers and Mathematics, 1989.
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同被引文献9

  • 1ROBBLANO L, SWEEDLER M. Subalgebra bases[ J]. Commutative Algebra, 1988, 1430:61-87.
  • 2KAPUR D, MADLENER K. A completion procedure for computing a canonical basis for a k-subalgebra[ C]. New York:Computers and Mathematics, 1989.
  • 3NORDBECK P. Canonical subalgebra bases in Non-commutative polynomial rings[C]. New York: ACM Press, 1998.
  • 4NORDBECK P. Canonical bases for subalgebras of factor algebras[ J]. Computer Science Journal of Moldora,1999,7:63-77.
  • 5LI Huishi. Looking for Grobner basis theory for ( almost). skew 2-nomial algebras [ J]. Journal of Symbolic Computation,2010,45:918-942.
  • 6LI Huishi. IMeading homogeneous algebras and Grobner bases[ J]. Advanced Lectures in Mathematics, 2009, 8 : 155-200.
  • 7BUCHBERGER B. Grobner bases: An algorithmic method in polynomial ideal theory[C]. Reidel Dordrecht:MultidimensionalSystems Theory, 1985.
  • 8MORA T. An introduction to commutative and noncommutative Grobner Bases[ J]. Theoretic Computer Science, 1994, 134:131-173.
  • 9GREEN E L. Noncommutative Grobner bases and projective resolutions[ J]. Proceedings of the Euroconference Computation-al Methods for Representations of Groups and Algebras, 1997,173 :29-60.

引证文献1

纯粹数学与应用数学
2011年 第6期

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