Equimultiple coefficient ideals - Lima, P. H.; Jorge Pérez, V. H. (MATHEMATICA SCANDINAVICA, 2017)
Let (R,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{1,… ,s}. The largest ideal L containing I such that e_i(I_p )=e_i(L_p ) for each i {1,… ,k} and each minimal prime 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 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.