The Igusa-Todorov function for comodules
Haim Mariana, Lanzilotta Marcelo, Mata Gustavo
TL;DR
This paper introduces the Igusa-Todorov function for finite dimensional comodules and characterizes left qcF coalgebras through this function's properties.
Contribution
It extends the Igusa-Todorov function to comodules and provides a characterization of left qcF coalgebras using this function.
Findings
A new definition of the Igusa-Todorov function for comodules
A characterization of left qcF coalgebras based on the function
Proof that the function is zero for certain comodules in left qcF coalgebras
Abstract
We define the Igusa-Todorov function in the context of finite dimensional comodules and prove that a coalgebra is left qcF if and only if it is left semiperfect and its Igusa-Todorov function on each right finite dimensional comodule is zero.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Rings, Modules, and Algebras · Advanced Topics in Algebra