Grade of ideals with respect to torsion theories
Mohsen Asgharzadeh, Massoud Tousi
TL;DR
This paper explores various homological methods to define and compare the grade of ideals with respect to torsion theories over commutative rings, including non-Noetherian cases.
Contribution
It introduces and compares multiple homological approaches to define the grade of ideals relative to torsion theories, extending classical notions to broader ring contexts.
Findings
Comparison of different grade definitions
Extension of grade concepts to non-Noetherian rings
Analysis of homological tools in torsion theories
Abstract
This paper deals with the notion of grade of ideals with respect to torsion theories defined via some homological tools such as Ext-modules, Koszul cohomology modules, \v{C}ech and local cohomology modules over commutative rings which are not necessarily Noetherian. We also compare these approaches of grade.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology