On Extensions of Right Symmetric Rings without Identity

@article{Shafee2014OnEO,
  title={On Extensions of Right Symmetric Rings without Identity},
  author={Basmah H. Shafee and S. Nauman},
  journal={Advances in Pure Mathematics},
  year={2014},
  volume={04},
  pages={665-673}
}
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. 

References

SHOWING 1-10 OF 13 REFERENCES
EXTENSIONS OF EXTENDED SYMMETRIC RINGS
Near-rings in which each element is a power of itself
Generalized symmetric rings
Reversible Rings with Involutions and Some Minimalities
Semigroups and rings whose zero products commute
A taxonomy of 2-primal rings
Semi-commutativity and the McCoy condition
Reversible and symmetric rings
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