Characterizing local rings via homological dimensions and regular sequences
Shokrollah Salarian, Sean Sather-Wagstaff, Siamak Yassemi
Abstract
Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If GC-dimension of M/IM is finite for all ideals I generated by an R-regular sequence of length at most d-t then either GC-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.
Create a lesson
Related papers
Ideals of 2-minors of nearly determinantal matrices
Takayuki Hibi, Francesco Navarra, Ayesha Asloob Qureshi
Intersection Product Formulas and Integral Dependence
Yairon Cid-Ruiz, Steven Dale Cutkosky
Uniform comparison of multiplier and test ideals for polynomials with affinely independent support
Takafumi Shibuta
Betti Sequences of Four-Generated Non-Almost-Symmetric Nearly Gorenstein Numerical Semigroup Rings
Zhi-Lin Zhang
Coherence and the Hilbert-syzygy identity for power series over valuation domains
Mohamed Amine Aouichaoui, Adam Jones, Yiding Wang
Geometry of Spaces of Subrings
Laura Cossu, Bruce Olberding, Giovanni Secreti