Octavio Mendoza

Stratifying systems via relative projective modules

ABSTRACT In this paper we point out that the “Process of standardization”, given in Dlab and Ringel (1992), and also the “Comparison method” given in Platzeck and Reiten (2001) can be generalized. To do so, we introduce the concept of relative projective stratifying system and prove a result from which the Theorem 2 in Dlab and Ringel (1992) and Proposition 2.1 in Ringel (1991) follows. #Communicated by A. Happel. ‡Dedicated to Raymundo Bautista on his 60th birthday.

C-filtered modules and proper costratifying systems

Abstract In this paper we define and study the notion of a proper costratifying system, which is a generalization of the so-called proper costandard modules to the context of stratifying systems. The proper costandard modules were defined by V. Dlab in his study of quasi-hereditary algebras (see Dlab, 1996 [D1] ).

On the Relative Socle for Stratifying Systems

Let A be a finite dimensional k-algebra, (Θ, ≤) be a stratifying system in mod(A) and ℱ(Θ) be the class of Θ-filtered A-modules. In this article, we give the definition and also study some of the properties of the relative socle in ℱ(Θ). We approach the relative socle in three ways. Namely, we view it as (1) a Θ-semisimple subobject of M having the largest Θ-length, (2) a maximal Θ-semisimple subobject of M, and (3) a minimal Θ-essential subobject of M.

Wide subcategories of finitely generated Λ-modules

We explore some properties of wide subcategories of the category modu(Λ) of finitely generated left Λ-modules, for some artin algebra Λ. In particular we look at wide finitely generated subcategories and give a connection with the class of standard modules and standardly stratified algebras. Furthermore, for a wide class 𝒳 in modu(Λ), we give necessary and sufficient conditions to see that 𝒳 = pres(P), for some projective Λ-module P; and finally, a connection with ring epimorphisms is given.

Relative Igusa-Todorov Functions and Relative Homological Dimensions

We develope the theory of E

Split-By-Nilpotent Extensions Algebras and Stratifying Systems

{\mathcal {E}}

Frobenius pairs in abelian categories: Correspondences with cotorsion pairs, exact model categories, and Auslander–Buchweitz contexts

-relative Igusa-Todorov functions in an exact IT-context (C,E)

On the Existence and Construction of Proper Costratifying Systems

({\mathcal {C}},{\mathcal {E}})

Stratifying systems via relative simple modules

(see Definition 2.1). In the case when C=mod(Λ)

An approach to the finitistic dimension conjecture

{\mathcal {C}}={\text {mod}}\, ({\Lambda })