| 单边单项式序下的SAGBI基 |
| |
| 引用本文： | 赵志琴.单边单项式序下的SAGBI基[J].纯粹数学与应用数学,2011,27(6):770-777. |
| |
| 作者姓名： | 赵志琴 |
| |
| 作者单位： | 中山大学新华学院经济与贸易系,广东广州,510520 |
| |
| 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...
|
| 关 键 词： | SM-基 子代数 SAGBI基 齐次SAGBI基 |
SAGBI bases under one-sided monomial orderings |
| |
| ZHAO Zhi-qin.SAGBI bases under one-sided monomial orderings[J].Pure and Applied Mathematics,2011,27(6):770-777. |
| |
| Authors: | ZHAO Zhi-qin |
| |
| Institution: | ZHAO Zhi-qin(Department of Economic and Trade,Xinhua College of Sun Yat-sen University,Guangzhou 510520,China) |
| |
| Abstract: | 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. |
| |
| Keywords: | SM-basis subalgebra SAGBI basis homogeneous SAGBI basis |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
