The Auslander bijections: How morphisms are determined by modules
CM Ringel - Bulletin of Mathematical Sciences, 2013 - Springer
Let Λ be an artin algebra. In his seminal Philadelphia Notes published in 1978, Auslander
introduced the concept of morphisms being determined by modules. Auslander was very …
introduced the concept of morphisms being determined by modules. Auslander was very …
[PDF][PDF] Left sections and the left part of an Artin algebra
I Assem - Colloq. Math, 2009 - usherbrooke.ca
Let A be an artin algebra. We are interested in studying the representation theory of A, thus
the category mod A of finitely generated right A-modules. For this purpose, we fix a full …
the category mod A of finitely generated right A-modules. For this purpose, we fix a full …
The Auslander-Reiten translation in submodule categories
C Ringel, M Schmidmeier - Transactions of the American Mathematical …, 2008 - ams.org
Let $\Lambda $ be an artin algebra or, more generally, a locally bounded associative
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …
algebra, and $\mathcal {S}(\Lambda) $ the category of all embeddings $(A\subseteq B) …
[PDF][PDF] The relative Auslander-Reiten theory of modules
CC Xi - preprint, 2005 - math0.bnu.edu.cn
Let A be an Artin algebra. As we know, the construction of the well-known Auslander-Reiten
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where the …
sequence is based on the natural (A, A)-bimodule A and the induced transpose, where 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 …
Morphisms determined by objects: The case of modules over artin algebras
CM Ringel - Illinois Journal of Mathematics, 2012 - projecteuclid.org
Let $\Lambda $ be an artin algebra. In his Philadelphia Notes, M. Auslander showed that
any homomorphism between $\Lambda $-modules is right determined by a $\Lambda …
any homomorphism between $\Lambda $-modules is right determined by a $\Lambda …
Irreducible morphisms in the bounded derived category
R Bautista, MJS Salorio - Journal of Pure and Applied Algebra, 2011 - Elsevier
We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …
A note on preprojective partitions over hereditary artin algebras
G Todorov - Proceedings of the American Mathematical Society, 1982 - ams.org
If $\Lambda $ is an artin algebra there is a partition of $\operatorname {ind}\Lambda $, the
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname …
category of indecomposable finitely generated $\Lambda $-modules, $\operatorname …
From subcategories to the entire module categories
R Hafezi - Forum Mathematicum, 2021 - degruyter.com
In this paper we show that how the representation theory of subcategories (of the category of
modules over an Artin algebra) can be connected to the representation theory of all modules …
modules over an Artin algebra) can be connected to the representation theory of all modules …
Cycles in module categories
A Skowroński - Finite dimensional algebras and related topics, 1994 - Springer
Let A be an artin algebra over a commutative artin ring R and mod A be the category of
finitely generated right A-modules. A cycle in mod A is a sequence of non-zero non …
finitely generated right A-modules. A cycle in mod A is a sequence of non-zero non …