… with unit induces a canonical recollement between the module categories over the rings , …
in categories of modules over triangular matrices rings. On the other hand, rings of the form …

… (in the category of rings), and hence we have a fully faithful exact functor, denoted by i * : A
/ … On the other hand, if we consider the restriction functor (see [Citation3, I.6]) j * : A ‐ Mod → …

… If 𝒞 is a triangulated category with translation functor Σ and Σ d ≅ id , we say that 𝒞 has
period d; if no such d exists, 𝒞 is said to have infinite period. Given a triangulated category 𝒞 , its …

… Such rings are called triangular matrix rings and appear in the … decomposition of algebras
and the direct sum of two rings. … study of functorially finite subcategories in functor categories. …

… as the construction of recollements and the study of functorially finite subcategories of
mod … as rings with several objects, we want to extend the notion of triangular matrix ring to …

… rings and $R = \left( \begin{smallmatrix} \Lambda & 0 \\ M & \Gamma \end{smallmatrix} \right)$
the triangular matrix ring … $\Gamma$ are finite dimensional algebras over an algebraically …

… subcategory induces a fully faithful functor between the absolute derived and the contraderived
categories, while the inclusion of a self-coresolving subcategory … the exact subcategory is …

… of recollements, and the study of functorially finite subcategories in functor categories. … finite
and left minimal s-approximation. We say that b is functorially finite if b is contravariantly finite …

… over an arbitrary ring to its trivial extension ring, and how to construct tilting modules over
triangular matrix rings… We denote by f-torsΛ the set of functorially finite torsion classes in mod Λ …

… rings and modules more abundant and interesting. So the properties of formal triangular
matrix rings and modules over … is Y , since q is an exact functor; but X may be not closed under …