On Extensions of Right Symmetric Rings without Identity

Basmah H. Shafee¹, S. Khalid Nauman^2*

¹Department of Mathematics, Umm Al-Qura University, Makkah, KSA.
²Department of Mathematics, King Abdulaziz University, Jeddah, KSA.

DOI: 10.4236/apm.2014.412075                

Abstract

Let us call a ring R (without identity) to be right symmetric if for any triple a,b,c,∈R abc = 0 then acb = 0. Such rings are neither symmetric nor reversible (in general) but are semicommutative. With an idempotent they take care of the sheaf representation as obtained by Lambek. Klein 4-rings and their several generalizations and extensions are proved to be members of such class of rings. An extension obtained is a McCoy ring and its power series ring is also proved to be a McCoy ring.

Keywords

Right (Left) Symmetric Rings, Klein 4-Rings, McCoy Rings

Conflicts of Interest

The authors declare no conflicts of interest.

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