| Abstract | In this paper, we generalize the notion of admissible order from finitely generated sub-monoids of M to M itself; assume that > is such an admissible order on M. We show that we can define leading power products, with respect to >, of elements in R^l, and thus the initial ideal gr(l) of an arbitrary ideal l subset R^l. If l is what we call a locally finitely generated ideal, then we show that l has a finite truncated Groebner basis up to any total degree. We give an example of a finitely generated homogeneous ideal which has a non-finitely generated initail lideal with respect to the lexicographic initial order > ??? on M. |
