RESEARCH ARTICLE

Koszulity and Koszul modules of dual extension algebras

  • Huanhuan LI 1 ,
  • Yunge XU , 2
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  • 1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China
  • 2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

Received date: 02 Mar 2016

Accepted date: 01 Jun 2016

Published date: 20 Apr 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let Aand Bbe algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that Tis Koszul if and only if both A and B are Koszul. Furthermore, we prove that an algebra is Koszul if and only if one of its iterated dual extension algebras is Koszul, if and only if all its iterated dual extension algebras are Koszul. Finally, we give a necessary and sufficient condition for a dual extension algebra to have the property that all linearly presented modules are Koszul modules, which provides an effective way to construct algebras with such a property.

Cite this article

Huanhuan LI , Yunge XU . Koszulity and Koszul modules of dual extension algebras[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 583 -596 . DOI: 10.1007/s11464-016-0601-4

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