TITLE:
NC-Rings and Some Commutativity Conditions
AUTHORS:
S. Khalid Nauman, Najat M. Muthana
KEYWORDS:
NC-Rings, NC-Rngs, Semi-Projective-Morita-Contexts, Right Ck-Goldie Rings
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.9 No.2,
February
28,
2019
ABSTRACT: 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.