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TitleLifting Standard Bases in Filtered Structures
Author(s) William W. Adams, Philippe Loustaunau
TypeTechnical Report, Misc
AbstractIn this paper we further study the theory of standard bases in filtered structures as introduced by Robbiano. In particular, we study the situation in which a commutative ring A is filtered by commutative ordered monoids \Delta and \Gamma in such a way that the \Gamma filtration refines the \Delta filtration. We use these results to determine conditions under which a \Delta standard basis can be lifted to a \Gamma standard basis. Finally, we interpret these results in three situations where the refinements are given by changing the status of the variables in a polynomial ring, refining a partial order on the monomials in a polynomial ring, and refining a filtration by an I-adic filtration for an ideal I in the ring A.
Translation No
Refereed No