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 I-adic filtration for an ideal I in the ring A. | Length | 24 |
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| Language | English | Year | 2005 | Translation |
No | Refereed |
No |
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