Details:
Title  Lifting Standard Bases in Filtered Structures  Author(s)  William W. Adams, Philippe Loustaunau  Type  Technical Report, Misc  Abstract  In 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 Iadic filtration for an ideal I in the ring A.  Length  24 
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 Language  English  Year  2005  Translation 
No  Refereed 
No 
