Finitistic dimension through infinite projective dimension

Abstract

We show that an Artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with a vanishing radical cube.

Finitistic dimension conjecture and conditions on ideals

“…The algebra was proved to have finite finitistic dimension in [4] by showing that ℓℓ ∞ A = 3. Here the notion ℓℓ ∞ A denotes the infinite-layer length of A, see [4] for details. In fact, one main result in [4] asserts that an artin algebra A has finite finitistic dimension whenever ℓℓ ∞ A ≤ 3, generalizing the known result for algebras with radical cube zero.…”

Una propuesta de cambio sustancial en la enseñanza de la matemática en la escuela elemental

“…Entonces, 3 es la relación entre 3 manzanas a 1 manzana. Esto no solo involucra pensamiento multiplicativo sino razonamiento proporcional [3]. La de¿nición formal del conjunto de los números racionales implica que el conjunto de los naturales sean un subconjunto propio.…”

“…El Lema (3.3) de [3] establece que, dado un Λ−módulo M , la familia de cocientes de M filtrados por S <∞ admite un único elemento maximal, que denotamos por C(M ). De este modo obtenemos la existencia de un epimorfis-…”

The derived dimensions and syzygy finite type

“…In [5,4], Huard, Lanzilotta and Hernández introduced the notion of the radical layer length associated with a torsion pair which is a generalization of the Loewy length. Let Λ be an artin algebra and V a set of some simple modules in mod Λ.…”