Abstract:

 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 subalgebras can be computed by means of effective algorithm, thereby the feasibility of constructing FS-bases under one-sided monomial ordering is clarified.

Key words: quotient algebra; subalgebra; FS-basis; homogeneous FS-basis