Equivalences induced by infinitely generated tilting modules

S Bazzoni - Proceedings of the American Mathematical Society, 2010 - ams.org
We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the
equivalences induced by a finitely generated tilting module over Artin algebras, to the case …

Infinitely generated complements to partial tilting modules

L Angeleri-Hügel, FU Coelho - Mathematical Proceedings of the …, 2002 - cambridge.org
Infinitely generated complements to partial tilting modules Page 1 Math. Proc. Camb. Phil.
Soc. (2002), 132, 89 c© Cambridge Philosophical Society DOI: 10.1017/S0305004101005394 …

[HTML][HTML] A note on relative tilting modules

J Wei - Journal of pure and applied algebra, 2010 - Elsevier
Bazzoni had given a simple characterization of infinitely generated n-tilting modules.
Though her method is even inapplicable to classical n-tilting modules over Artin algebras …

Tilting objects in abelian categories and quasitilted rings

R Colpi, K Fuller - Transactions of the American Mathematical Society, 2007 - ams.org
D. Happel, I. Reiten and S. Smalø initiated an investigation of quasitilted artin $ K $-algebras
that are the endomorphism rings of tilting objects in hereditary abelian categories whose …

Tilted algebras and short chains of modules

A Jaworska, P Malicki, A Skowroński - Mathematische Zeitschrift, 2013 - Springer
We provide an affirmative answer for the question raised almost 20 years ago in Reiten et
al.(Proc. Am. Math. Soc. 117: 343–354, 1993) concerning the characterization of tilted artin …

[引用][C] On a Partial Order of Tilting Modules: Dedicated to the memory of Sheila Brenner

D Happel, L Unger - Algebras and Representation Theory, 2005 - Springer
Let be an Artin algebra over a commutative Artin ring R and let mod be the category of
finitely generated left-modules. For a module M∈ mod we denote by pd M the projective …

Existence criteria and construction methods for certain classes of tilting modules

H Valenta - Communications in Algebra, 1994 - Taylor & Francis
Tilting modules are an essential tool of representation theory and have been studied by
several authors. In the present paper we state an existence theorem for tilting modules …

[HTML][HTML] Perpendicular categories of infinite dimensional partial tilting modules and transfers of tilting torsion classes

R Colpi, A Tonolo, J Trlifaj - Journal of Pure and Applied Algebra, 2007 - Elsevier
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 …

Tilting modules over trivial extensions of artin algebras

JI Miyachi - Communications in Algebra, 1985 - Taylor & Francis
Tilting modules over trivial extensions of artin algebras Page 1 COMMUNICATIONS IN
ALGEBRA, 13(6), 1319-1326 (1985) TILTING MODULES OVER TRIVIAL EXTENSIONS OF …

Derived equivalence induced by infinitely generated 𝑛-tilting modules

S Bazzoni, F Mantese, A Tonolo - Proceedings of the American …, 2011 - ams.org
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 …