Vol. 14, No. 3, 2021

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Cohen–Macaulay test ideals over rings of finite and countable Cohen–Macaulay type

Julian Benali, Shrunal Pothagoni and Rebecca R.G.

Vol. 14 (2021), No. 3, 413–430
Abstract

R.G. and Pérez proved that under certain conditions the test ideal of a module closure agrees with the trace ideal of the module closure. We use this fact to compute the test ideals of various rings with respect to the closures coming from their indecomposable maximal Cohen–Macaulay modules. We also give an easier way to compute the test ideal of a hypersurface ring in three variables coming from a module with a particular type of matrix factorization.

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Keywords
maximal Cohen–Macaulay modules, trace ideals, test ideals, ADE singularities
Mathematical Subject Classification
Primary: 13C14, 13P99
Secondary: 13F70, 13H10
Milestones
Received: 17 July 2020
Revised: 15 February 2021
Accepted: 23 February 2021
Published: 17 July 2021

Communicated by Scott T. Chapman
Authors
Julian Benali
Department of Mathematical Sciences
George Mason University
Fairfax, VA
United States
Shrunal Pothagoni
Department of Mathematical Sciences
George Mason University
Fairfax, VA
United States
Rebecca R.G.
Department of Mathematical Sciences
George Mason University
Fairfax, VA
United States