On Extensions of Right Symmetric Rings without Identity

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.

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Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Shafee, B. and Nauman, S. (2014) On Extensions of Right Symmetric Rings without Identity. Advances in Pure Mathematics, 4, 665-673. doi: 10.4236/apm.2014.412075.

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