On extensions of matrix rings with skew Hochschild 2-cocycles  

作　　者：Chan Yong HONG Nam Kyun KIM Tai Keun KWAK Yang LEE 

机构地区：[1]Department of Mathematics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 02447, Korea [2]School of Basic Sciences, Hanbat National University, Daejeon 34158, Korea [3]Department of Mathematics, Daejin University, Pocheon 11159, Korea [4]Department of Mathematics, Pusan National University, Pusan 46241, Korea

出　　处：《Frontiers of Mathematics in China》2016年第4期869-900,共32页中国高等学校学术文摘·数学（英文）

摘　　要：We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible （or semicommutative） rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible （or semicommutative） rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.

关 键 词：Skew Hochschild extensions matrix rings skew triangular matrix rings （uniquely） clean rings symmetric rings 

分 类 号：O153.3[理学—数学] TN911.23[理学—基础数学]