Tilting and trivial extensions
Q Chen, M Gong, W Rump - Archiv der Mathematik, 2009 - Springer
The trivial extensions of a quasi-abelian category by means of a fully exact endofunctor are
again quasi-abelian. Using the one-to-one correspondence between quasi-abelian …
again quasi-abelian. Using the one-to-one correspondence between quasi-abelian …
On the heart of a faithful torsion theory
R Colpi, E Gregorio, F Mantese - Journal of Algebra, 2007 - Elsevier
In [R. Colpi, KR Fuller, Tilting objects in abelian categories and quasitilted rings, Trans.
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …
*-Modules, tilting, and almost abelian categories
W Rump - Communications in Algebra, 2001 - Taylor & Francis
The concept of*-module arose from a remarkable converse of the tilting theorem due to
Menini and Orsatti [25] who essentially proved that for suitable full subcategories G & R-Mod …
Menini and Orsatti [25] who essentially proved that for suitable full subcategories G & R-Mod …
Exact categories and infinite tilting
W Rump - Communications in Algebra, 2021 - Taylor & Francis
It is proved that any tilting adjunction is completely described by an exact category with a
coherence property and the closure condition that exact sequences are acyclic. The …
coherence property and the closure condition that exact sequences are acyclic. The …
Tilting modules and -modules
R Colpi - Communications in Algebra, 1993 - research.unipd.it
C. Menini and A. Orsatti [Rend. Sem. Mat. Univ. Padova 82 (1989), 203--231 (1990);
MR1049594 (91h: 16026)] introduced∗-modules in order to characterize equivalences …
MR1049594 (91h: 16026)] introduced∗-modules in order to characterize equivalences …
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 …
that are the endomorphism rings of tilting objects in hereditary abelian categories whose …
Weakly tilting bimodules
E Gregorio, A Tonolo - 2001 - degruyter.com
Tilting modules arose from representation theory of algebras and are known to furnish
equivalences between categories of modules. We single out some weaker properties which …
equivalences between categories of modules. We single out some weaker properties which …
Topological tilting modules
E Gregorio - Communications in Algebra, 2001 - Taylor & Francis
Tilting modules appear in a variety of ways: their first definition was in the context of finite
dimensional algebras over a field. Later, they appeared naturally in applications of the …
dimensional algebras over a field. Later, they appeared naturally in applications of the …
Homologically finite subcategories
M Auslander, I Reiten - Representations of algebras and related …, 1992 - cambridge.org
Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …
Tilting preenvelopes and cotilting precovers in general Abelian categories
We consider an arbitrary Abelian category A and a subcategory T closed under extensions
and direct summands, and characterize those T that are (semi-) special preenveloping in A; …
and direct summands, and characterize those T that are (semi-) special preenveloping in A; …