Residually faithful modules and the Cohen-Macaulay type of idealizations
Shiro Goto, Shinya Kumashiro, Nguyen Thi Hong Loan
TL;DR
This paper investigates the Cohen-Macaulay type of idealizations of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings, connecting it to Ulrich modules and residually faithful modules.
Contribution
It introduces new insights into the Cohen-Macaulay type of idealizations, linking it to Ulrich modules and residually faithful modules, and explores extremal cases.
Findings
Relation between Cohen-Macaulay type and Ulrich modules
Connection to residually faithful modules and closed ideals
Analysis of extremal cases in idealizations
Abstract
The Cohen-Macaulay type of idealizations of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings is explored. There are two extremal cases, one of which is closely related to the theory of Ulrich modules \cite{BHU, GOTWY1, GOTWY2, GTT2}, and the other one is closely related to the theory of residually faithful modules and the theory of closed ideals \cite{BV}.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Pharmacological Receptor Mechanisms and Effects