APM  Vol.4 No.12 , December 2014
On Extensions of Right Symmetric Rings without Identity
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.
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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