An approach to the finitistic dimension conjecture.

DOI10.1016/J.JALGEBRA.2008.02.008zbMath1148.16004arXiv0710.2328OpenAlexW2963126833WikidataQ123361297 ScholiaQ123361297MaRDI QIDQ933382

Octavio Mendoza, François Huard, Marcelo Américo Lanzilotta

Publication date: 21 July 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.2328

zbMATH Keywords

projective dimensionfinitistic dimensionstratifying systems

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (23)

Idempotent ideals and the Igusa-Todorov functions ⋮ Relative Igusa-Todorov functions and relative homological dimensions ⋮ Generalised Igusa-Todorov functions and Lat-Igusa-Todorov algebras ⋮ Layer lengths, torsion theories and the finitistic dimension ⋮ Igusa-Todorov functions for Artin algebras ⋮ The Igusa-Todorov function for comodules ⋮ Convex subquivers and the finitistic dimension ⋮ Unnamed Item ⋮ Igusa-Todorov \(\phi\) function for truncated path algebras ⋮ The Igusa-Todorov \(\phi \)-dimension on Morita context algebras ⋮ Igusa-Todorov and LIT algebras on Morita context algebras ⋮ Generalized Igusa-Todorov function and finitistic dimensions. ⋮ Self-injective right Artinian rings and Igusa Todorov functions. ⋮ Recollements and homological dimensions ⋮ Gaps for the Igusa-Todorov function ⋮ Pullback diagrams, syzygy finite classes and Igusa-Todorov algebras ⋮ Igusa-Todorov functions for radical square zero algebras ⋮ Idealized Extensions of Artin Algebras and Finitistic Dimensions ⋮ Split-By-Nilpotent Extensions Algebras and Stratifying Systems ⋮ Stratifying systems through \(\tau\)-tilting theory ⋮ Homological dimensions of the extension algebras of monomial algebras. ⋮ THE FINITISTIC DIMENSION AND CHAIN CONDITIONS ON IDEALS ⋮ The \(\phi\)-dimension: a new homological measure.

Cites Work

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• Applications of stratifying systems to the finitistic dimension.
• Tilting categories with applications to stratifying systems.
• Stratifying systems via relative simple modules.
• On the finitistic dimension conjecture. I: Related to representation-finite algebras.
• On Standardly Stratified Algebras
• Finitistic dimension of standardly stratified algebras
• The finitistic dimension conjectures -- a tale of 3.5 decades
• Stratifying Systems via Relative Projective Modules

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