Tilted algebras and short chains of modules
Alicja Jaworska, Piotr Malicki, Andrzej Skowro\'nski
TL;DR
This paper characterizes tilted artin algebras by the existence of a sincere finitely generated module that is not the middle of a short chain, resolving a question from twenty years ago.
Contribution
It provides an affirmative answer to a long-standing open problem in the theory of tilted algebras.
Findings
Characterization of tilted artin algebras via sincere modules
Resolution of a twenty-year-old open question
Identification of modules not forming short chains
Abstract
We provide an affirmative answer for the question raised almost twenty years ago concerning the characterization of tilted artin algebras by the existence of a sincere finitely generated module which is not the middle of a short chain.
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