Finitistic Dimension Conjecture and Conditions on Ideals
Jiaqun Wei
TL;DR
This paper introduces Igusa-Todorov classes and explores conditions on special ideals that imply finiteness properties, contributing to the proof of the finitistic dimension conjecture in certain cases.
Contribution
It establishes new conditions on ideals that ensure finiteness properties related to the finitistic dimension conjecture.
Findings
Igusa-Todorov classes are connected to the finitistic dimension conjecture.
Conditions on special ideals imply finiteness conditions on modules.
Results support the conjecture in specific algebraic contexts.
Abstract
The notion of Igusa-Todorov classes is introduced in connection with the finitistic dimension conjecture. As application we consider conditions on special ideals which imply the Igusa-Todorov and other finiteness conditions on modules proving the finitistic dimension conjecture and related conjectures in those cases.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Commutative Algebra and Its Applications