Cohen-Macaulayness of Rees Algebras of Modules
Kuei-Nuan Lin
TL;DR
This paper establishes sufficient conditions for Rees algebras of modules to be Cohen-Macaulay, extending known results from ideals and employing generic Bourbaki ideals for the proof.
Contribution
It generalizes Cohen-Macaulayness criteria from ideals to modules, involving significant technical development and the use of generic Bourbaki ideals.
Findings
Provided new sufficient conditions for Cohen-Macaulayness of Rees algebras of modules.
Extended the Cohen-Macaulayness results from ideals to modules.
Utilized the technique of generic Bourbaki ideals in the proof.
Abstract
We provide the sufficient conditions for Rees algebras of modules to be Cohen-Macaulay, which has been proven in the case of Rees algebras of ideals by Johnson-Ulrich and Goto-Nakamura-Nishida. As it turns out the generalization from ideals to modules is not just a routine generalization, but requires a great deal of technical development. We use the technique of generic Bourbaki ideals introduced by Simis, Ulrich and Vasconcelos to obtain the Cohen-Macaulayness of Rees Algebras of modules.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Cholinesterase and Neurodegenerative Diseases