单边单项式序下的FS-基

FS-basis under one-sided monomial orderings

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商代数的子代数在双边单项式序下经典的FS-基理论可完整地推广到R的任一商代数R/I的子代数上。特别地,对于一类N-分次代数R/I,给出计算有限n-截断FS-基的有效算法,从而阐明了在单边单项式序下构造FS-基的可行性。

Let K be a field, R a K-algebra with an SM-basis B, and let 〈 be a one-sided （i. e. left or right） monomial ordering on B. Then the classical Factor-SAGBI basis theory （w. r. t a two-sided monomial ordering） for subalgebra of commutative polynomial algebras and noncommutative free algebras can be completely generalized to subalgebras of any quotient algebra R/I of R. In particular, for a class of N-graded quotient algebras, finite n-truncated FS-bases for subal-gebras can be computed by means of effective algorithm, thereby the feasibility of constructing FS-bases under one-si-ded monornial ordering is clarified.