About Multiplicities and Applications to Bezout Numbers
About Multiplicities and Applications to Bezout Numbers
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:= …