Anzeige
Erschienen in:
2017 | OriginalPaper | Buchkapitel
About Multiplicities and Applications to Bezout Numbers
verfasst von : M. Azeem Khadam, Peter Schenzel
Erschienen in: Homological and Computational Methods in Commutative Algebra
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
Let \((A,\mathfrak{m}, \mathbb{k})\) denote a local Noetherian ring and \(\mathfrak{q}\) an ideal such that \(\ell_{A}(M/\mathfrak{q}M) <\infty\) for a finitely generated \(A\)-module \(M\). Let \(\underline{a} = a_{1},\ldots,a_{d}\) denote a system of parameters of \(M\) such that \(a_{i} \in \mathfrak{q}^{c_{i}}\setminus \mathfrak{q}^{c_{i}+1}\) for \(i = 1,\ldots,d\). It follows that \(\chi:= e_{0}(\underline{a};M) - c \cdot e_{0}(\mathfrak{q};M) \geq 0\), where \(c = c_{1} \cdot \ldots \cdot c_{d}\). The main results of the report are a discussion when \(\chi = 0\) resp. to describe the value of \(\chi\) in some particular cases. Applications concern results on the multiplicity \(e_{0}(\underline{a};M)\) and applications to Bezout numbers.