NC-Rings and Some Commutativity Conditions  

作　　者：S. Khalid Nauman Najat M. Muthana 

机构地区：[1]Department of Mathematics, King Abdulaziz University, Jeddah, KSA

出　　处：《Advances in Pure Mathematics》2019年第2期143-163,共21页理论数学进展（英文）

摘　　要：Sum of two nilpotent elements in a ring may not be nilpotent in general, but for commutative rings this sum is nilpotent. In between commutative and non-commutative rings there are several types of rings in which this property holds. For instance, reduced, NI, AI (or IFP), 2-primal, reversible and symmetric, etc. We may term these types of rings as nearby commutative rings (in short NC-rings). In this work we have studied properties and various characterizations of such rings as well as rngs. As applications, we have investigated some commutativity conditions by involving semi-projective-Morita-contexts and right Ck-Goldie rings.Sum of two nilpotent elements in a ring may not be nilpotent in general, but for commutative rings this sum is nilpotent. In between commutative and non-commutative rings there are several types of rings in which this property holds. For instance, reduced, NI, AI (or IFP), 2-primal, reversible and symmetric, etc. We may term these types of rings as nearby commutative rings (in short NC-rings). In this work we have studied properties and various characterizations of such rings as well as rngs. As applications, we have investigated some commutativity conditions by involving semi-projective-Morita-contexts and right Ck-Goldie rings.

关 键 词：NC-Rings NC-Rngs Semi-Projective-Morita-Contexts Right Ck-Goldie RINGS 

分 类 号：O1[理学—数学]