ON A RING PROPERTY UNIFYING REVERSIBLE AND RIGHT DUO RINGS

Title & Authors
ON A RING PROPERTY UNIFYING REVERSIBLE AND RIGHT DUO RINGS
Kim, Nam Kyun; Lee, Yang;

Abstract
The concepts of reversible, right duo, and Armendariz rings are known to play important roles in ring theory and they are independent of one another. In this note we focus on a concept that can unify them, calling it a right Armendarizlike ring in the process. We first find a simple way to construct a right Armendarizlike ring but not Armendariz (reversible, or right duo). We show the difference between right Armendarizlike rings and strongly right McCoy rings by examining the structure of right annihilators. For a regular ring R, it is proved that R is right Armendarizlike if and only if R is strongly right McCoy if and only if R is Abelian (entailing that right Armendarizlike, Armendariz, reversible, right duo, and IFP properties are equivalent for regular rings). It is shown that a ring R is right Armendarizlike, if and only if so is the polynomial ring over R, if and only if so is the classical right quotient ring (if any). In the process necessary (counter)examples are found or constructed.
Keywords
right Armendarizlike ring;polynomial ring;reversible ring;right duo ring;Armendariz ring;strongly right McCoy ring;regular ring;
Language
English
Cited by
1.
MCCOY CONDITION ON IDEALS OF COEFFICIENTS,;;;;

대한수학회보, 2013. vol.50. 6, pp.1887-1903
1.
MCCOY CONDITION ON IDEALS OF COEFFICIENTS, Bulletin of the Korean Mathematical Society, 2013, 50, 6, 1887
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