TITLE:
On Extensions of Right Symmetric Rings without Identity
AUTHORS:
Basmah H. Shafee, S. Khalid Nauman
KEYWORDS:
Right (Left) Symmetric Rings, Klein 4-Rings, McCoy Rings
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.12,
December
29,
2014
ABSTRACT: Let us
call a ring R (without identity) to
be right symmetric if for any triple a,b,c,∈Rabc = 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.