Classification of module categories for SO(3)2

Classification of Split Ttf-triples in Module Categories

In our work [9], we complete Jans’ classification of TTF-triples [8] by giving a precise description of those two-sided ideals of a ring associated to one-sided split TTF-triples in the corresponding module category.

Tilting in module categories

Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples ...

Fuzzy projective modules and tensor products in fuzzy module categories

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

Recollements of (derived) module categories

Recollements of abelian, resp. triangulated, categories are exact sequences of abelian, resp. triangulated, categories where the inclusion functor as well as the quotient functor have left and right adjoints. They appear quite naturally in various settings and are omnipresent in representation theory. Recollements which all categories involved are module categories (abelian case) or derived cat...

Picard Groups for Derived Module Categories