On Extensions of Right Symmetric Rings without Identity

DOI: 10.4236/apm.2014.412075   PDF   HTML   XML   2,626 Downloads   3,185 Views   Citations

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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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