On the effective membership problem for polynomial ideals

Kapitel i bok, 2017

We discuss the possibility of representing elements in polynomial ideals in ℂN with optimal degree bounds. Classical theorems due to Macaulay and Max Noether say that such a representation is possible under certain conditions on the variety of the associated homogeneous ideal. We present some variants of these results, as well as generalizations to subvarieties of ℂN.