On Gorenstein coalgebras  

作　　者：Xuerong FU Hailou YAO 

机构地区：[1]College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

出　　处：《Frontiers of Mathematics in China》2016年第4期845-867,共23页中国高等学校学术文摘·数学（英文）

基　　金：The authers sincerely thank the referees and Prof. Dingguo Wang for the careful reading and helpful suggestions in improving the paper. This work was supported by the National Natural Science Foundation of China （Grant No. 11271119） and the Natural Science Foundation of Beijing （Grant No. 1122002）.

摘　　要：We investigate the comodule representation category over the Morita-Takeuchi context coalgebra F and study the Gorensteinness of F. Moreover, we determine explicitly all Gorenstein injective comodules over the Morita-Takeuchi context coalgebra F and discuss the localization in Gorenstein coalgebras. In particular, we describe its Gabriel quiver and carry out some examples when the Morita-Takeuchi context coalgebra is basic.We investigate the comodule representation category over the Morita-Takeuchi context coalgebra F and study the Gorensteinness of F. Moreover, we determine explicitly all Gorenstein injective comodules over the Morita-Takeuchi context coalgebra F and discuss the localization in Gorenstein coalgebras. In particular, we describe its Gabriel quiver and carry out some examples when the Morita-Takeuchi context coalgebra is basic.

关 键 词：Gorenstein coalgebra Gorenstein injective comodule Gabriel quiver 

分 类 号：O153.3[理学—数学] O154.1[理学—基础数学]