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Birkenmeier, G.F., Heatherly, H.E. and Lee, E.K. (1993) Completely Prime Ideals and Associated Radicals, Ring Theory (Granville, OH 1992). World Scientific Publisher, River Edge, NJ, 102-129.

has been cited by the following article:

  • 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.