2012
DOI: 10.1093/qmath/has034
|View full text |Cite
|
Sign up to set email alerts
|

Modules Not Being the Middle of Short Chains

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1

Citation Types

0
2
0

Year Published

2014
2014
2019
2019

Publication Types

Select...
3
1

Relationship

0
4

Authors

Journals

citations
Cited by 4 publications
(2 citation statements)
references
References 25 publications
0
2
0
Order By: Relevance
“…Clearly, we may realistically hope to describe the structure of Supp(M ) only for modules M having some distinguished properties. For example, if M is a directing module in ind A, then the support algebra Supp(M ) of M over an algebra A is a tilted algebra End H (T ), for a hereditary algebra H and a tilting module T in mod H, and M is isomorphic to the image Hom H (T, I) of an indecomposable injective module I in mod H via the functor Hom H (T, −) : mod H → mod End H (T ) (see [49] and [23], [24] for the corresponding result over arbitrary artin algebra).…”
Section: Preliminariesmentioning
confidence: 99%
“…Clearly, we may realistically hope to describe the structure of Supp(M ) only for modules M having some distinguished properties. For example, if M is a directing module in ind A, then the support algebra Supp(M ) of M over an algebra A is a tilted algebra End H (T ), for a hereditary algebra H and a tilting module T in mod H, and M is isomorphic to the image Hom H (T, I) of an indecomposable injective module I in mod H via the functor Hom H (T, −) : mod H → mod End H (T ) (see [49] and [23], [24] for the corresponding result over arbitrary artin algebra).…”
Section: Preliminariesmentioning
confidence: 99%
“…In connection with the final part of the above proof, we mention that, by a recent result proved by Jaworska, Malicki and Skowroński in [29], an algebra A is a tilted algebra if and only if there exists a sincere module M in mod A such that for any module X in ind A, we have Hom A (X, M ) = 0 or Hom A (M, τ A X) = 0. Moreover, all modules M in a module category mod A not being the middle of short chains have been described completely in [30].…”
Section: (V) No Proper Full Convex Subquiver Of ∆ Satisfies (I)-(iv)mentioning
confidence: 99%