Author(s)

S. Khalid Nauman, Najat M. Muthana

Department of Mathematics, King Abdulaziz University, Jeddah, KSA.

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 C_k-Goldie rings.

NC-Rings, NC-Rngs, Semi-Projective-Morita-Contexts, Right C_k-Goldie Rings

Nauman, S. and Muthana, N. (2019) NC-Rings and Some Commutativity Conditions. Advances in Pure Mathematics, 9, 143-163. doi: 10.4236/apm.2019.92008.