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Volume 30, Issue 4
The Almost Split Sequences for Trivial Extensions of Hereditary Algebras

Yulin Zhang & Hailou Yao

DOI: 10.13447/j.1674-5647.2014.04.10

Commun. Math. Res., 30 (2014), pp. 369-378.

Published online: 2021-05

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  • Abstract

Let $A$ be a basic hereditary artin algebra and $R = A \ltimes Q$ be the trivial extension of $A$ by its minimal injective cogenerator $Q$. We construct some right (left) almost split morphisms and irreducible morphisms in mod$R$ through the corresponding morphisms in mod$A$. Furthermore, we can determine its almost split sequences in mod$R$.

  • Keywords

hereditary algebra, trivial extension, AR sequence, irreducible morphism.

  • AMS Subject Headings

16G20, 16G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-30-369, author = {Zhang , Yulin and Yao , Hailou}, title = {The Almost Split Sequences for Trivial Extensions of Hereditary Algebras}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {30}, number = {4}, pages = {369--378}, abstract = {

Let $A$ be a basic hereditary artin algebra and $R = A \ltimes Q$ be the trivial extension of $A$ by its minimal injective cogenerator $Q$. We construct some right (left) almost split morphisms and irreducible morphisms in mod$R$ through the corresponding morphisms in mod$A$. Furthermore, we can determine its almost split sequences in mod$R$.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.10}, url = {http://global-sci.org/intro/article_detail/cmr/18959.html} }
TY - JOUR T1 - The Almost Split Sequences for Trivial Extensions of Hereditary Algebras AU - Zhang , Yulin AU - Yao , Hailou JO - Communications in Mathematical Research VL - 4 SP - 369 EP - 378 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.13447/j.1674-5647.2014.04.10 UR - https://global-sci.org/intro/article_detail/cmr/18959.html KW - hereditary algebra, trivial extension, AR sequence, irreducible morphism. AB -

Let $A$ be a basic hereditary artin algebra and $R = A \ltimes Q$ be the trivial extension of $A$ by its minimal injective cogenerator $Q$. We construct some right (left) almost split morphisms and irreducible morphisms in mod$R$ through the corresponding morphisms in mod$A$. Furthermore, we can determine its almost split sequences in mod$R$.

Zhang , Yulin and Yao , Hailou. (2021). The Almost Split Sequences for Trivial Extensions of Hereditary Algebras. Communications in Mathematical Research . 30 (4). 369-378. doi:10.13447/j.1674-5647.2014.04.10
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