EXTENSIONS OF EXTENDED SYMMETRIC RINGS

Title & Authors
EXTENSIONS OF EXTENDED SYMMETRIC RINGS
Kwak, Tai-Keun;

Abstract
An endomorphism $\small{{\alpha}}$ of a ring R is called right(left) symmetric if whenever abc=0 for a, b, c $\small{{\in}}$ R, $\small{ac{\alpha}(b)=0({\alpha}(b)ac=0)}$. A ring R is called right(left) $\small{{\alpha}-symmetric}$ if there exists a right(left) symmetric endomorphism $\small{{\alpha}}$ of R. The notion of an $\small{{\alpha}-symmetric}$ ring is a generalization of $\small{{\alpha}-rigid}$ rings as well as an extension of symmetric rings. We study characterizations of $\small{{\alpha}-symmetric}$ rings and their related properties including extensions. The relationship between $\small{{\alpha}-symmetric}$ rings and(extended) Armendariz rings is also investigated, consequently several known results relating to $\small{{\alpha}-rigid}$ and symmetric rings can be obtained as corollaries of our results.
Keywords
reduced rings;symmetric rings;(extended) Armendariz rings;
Language
English
Cited by
1.
On Extensions of Right Symmetric Rings without Identity, Advances in Pure Mathematics, 2014, 04, 12, 665
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