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

Author

Julian Benali, Shrunal Pothagoni, and R G Rebecca

Subjects
Pure mathematics, Ring (mathematics), Trace (linear algebra), Hypersurface, Mathematics::Commutative Algebra, General Mathematics, Countable set, Ideal (ring theory), Type (model theory), Indecomposable module, Matrix decomposition, Mathematics
Abstract

R.G. and Perez 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.

Published
2021

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