@article{Lima_Jorge Pérez_2017, title={Equimultiple coefficient ideals}, volume={121}, url={https://www.mscand.dk/article/view/25988}, DOI={10.7146/math.scand.a-25988}, abstractNote={<p>Let $(R,\mathfrak {m})$ be a quasi-unmixed local ring and $I$ an equimultiple ideal of $R$ of analytic spread $s$. In this paper, we introduce the equimultiple coefficient ideals. Fix $k\in \{1,\dots ,s\}$. The largest ideal $L$ containing $I$ such that $e_{i}(I_{\mathfrak{p} })=e_{i}(L_{\mathfrak{p} })$ for each $i \in \{1,\dots ,k\}$ and each minimal prime $\mathfrak{p} $ of $I$ is called the $k$-th equimultiple coefficient ideal denoted by $I_{k}$. It is a generalization of the coefficient ideals introduced by Shah for the case of $\mathfrak {m}$-primary ideals. We also see applications of these ideals. For instance, we show that the associated graded ring $G_{I}(R)$ satisfies the $S_{1}$ condition if and only if $I^{n}=(I^{n})_{1}$ for all $n$.</p>}, number={1}, journal={MATHEMATICA SCANDINAVICA}, author={Lima, P. H. and Jorge Pérez, V. H.}, year={2017}, month={Sep.}, pages={5–18} }