Abstract
A right ideal I of a ring R is called a comparizer right ideal if for all right ideals A, B of R, either A ⊆ B or BI ⊆ A. For every ring R there exists the largest comparizer ideal C 1(R) of R, and higher comparizer ideals C α(R) can be defined inductively. In this paper, comparizer right ideals and relationships between the iterated comparizer ideal and some classical radicals of R are studied. Obtained results generalize some properties of right chain rings, right distributive rings, right Bezout rings and rings with comparability.
Mathematics Subject Classification:
Acknowledgments
The first author was supported by KBN Grant 5 P03A 04120. Most of this work was done when the first author was visiting University of Duisburg. Here he wishes to thank for the hospitality given by the members of the Department of Mathematics.
Notes
#Communicated by E. Puczyłowski.