Let TR be a right n-tilting module over an arbitrary associative ring R. In this paper we prove
that there exists a n-tilting module T′ R equivalent to TR which induces a derived …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

Let C be a triangulated category with shift functor [1] and R a rigid subcategory of C. We
introduce the notions of two-term R [1]-rigid subcategories, two-term (weak) R [1]-cluster …

In Corollary 4.2 we showed that for subcategories C of mod II closed under extensions of the
form C= Sub M there are only a finite number of nonisomorphic indecomposable objects in …

Tilting theory has been a very important tool in the classification of finite dimensional
algebras of finite and tame representation type, as well as, in many other branches of …

Let $\mathcal B $ be an extriangulated category with enough projectives and enough
injectives. We define a proper $ m $-term subcategory $\mathcal G $ on $\mathcal B …

Let R be a ring and P be an (infinite dimensional) partial tilting module. We show that the
perpendicular category of P is equivalent to the full module category Mod-S where S= End …

Let $ T_R $ be a right $ n $-tilting module over an arbitrary associative ring $ R $. In this
paper we prove that there exists an $ n $-tilting module $ T'_R $ equivalent to $ T_R $ which …

We introduce a notion of generalized Auslander–Reiten duality on a Hom-finite Krull–
Schmidt exact category 𝒞. This duality induces the generalized Auslander–Reiten …

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-
Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension …