单边单项式序下的SAGBI基

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.