Affiliation:
1. Department of Applied Mathematics, College of Information Science and Technology, Hainan University, Haikou570228, P. R. China
Abstract
AbstractLet {K\langle X\rangle=K\langle X_{1},\ldots,X_{n}\rangle}
be the free algebra generated by {X=\{X_{1},\ldots,X_{n}\}} over a
field K. It is shown that, with respect to any weighted
{\mathbb{N}}-gradation attached to {K\langle X\rangle}, minimal homogeneous
generating sets for finitely generated graded two-sided ideals of
{K\langle X\rangle} can be algorithmically computed, and that if an ungraded
two-sided ideal I of {K\langle X\rangle} has a finite Gröbner basis {{\mathcal{G}}} with
respect to a graded monomial ordering on {K\langle X\rangle}, then a minimal
standard basis for I can be computed via computing a minimal
homogeneous generating set of the associated graded ideal
{\langle\mathbf{LH}(I)\rangle}.
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