2021/12/18 by Meng Cheng, Meng, Cheng
Mathematics · #13H15 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2112.09849
openalex publication_date 2021/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of strongly Lech-independent ideals as a generalization of Lech-independent ideals defined by Lech and Hanes, and use this notion to derive inequalities on multiplicities of ideals. In particular we prove that if (R,\mathfrakm) → (S,\mathfrakn) is a flat local extension of local rings with dim R = dim S, the completion of S is the completion of a standard graded ring over a field k with respect to the homogeneous maximal ideal, and the completion of \mathfrakmS is the completion of a homogeneous ideal, then e(R) ≤ e(S).