Koszulity and Koszul modules of dual extension algebras  

作　　者：Huanhuan LI Yunge XU 

机构地区：[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

出　　处：《Frontiers of Mathematics in China》2017年第3期583-596,共14页中国高等学校学术文摘·数学（英文）

基　　金：The first author is and encouragement. The authors thank grateful to Professor Yu Ye for helpful discussion the anonymous referees for their very helpful suggestions to improve this paper. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571341, 11371186）.

摘　　要：Let A and B be algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that T is 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.Let A and B be algebras, and let T be the dual extension algebra of A and B. We provide a different method to prove that T is 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.

关 键 词：Dual extension linearly presented Koszul algebra Koszul module 

分 类 号：T[一般工业技术]