On extensions of matrix rings with skew Hochschild 2-cocycles

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

作者机构：Department of Mathematics and Research Institute for Basic Sciences Kyung Hee University Seoul 02447 Korea School of Basic Sciences Hanbat National University Daejeon 34158 Korea Department of Mathematics Daejin University Pocheon 11159 Korea Department of Mathematics Pusan National University Pusan 46241 Korea 

出 版 物：《Frontiers of Mathematics in China》 (中国高等学校学术文摘·数学（英文）)

年 卷 期：2016年第11卷第4期

页      面：869-900页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 081101[工学-控制理论与控制工程] 0701[理学-数学] 0811[工学-控制科学与工程] 

基　　金：supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education 

主　　题：Skew Hochschild extensions matrix rings skew triangular matrix rings (uniquely) clean rings symmetric rings 

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.