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eISSN 0454-8124
pISSN 1225-6951

### Article

Kyungpook Mathematical Journal 2021; 61(1): 11-21

Published online March 31, 2021

Copyright © Kyungpook Mathematical Journal.

### Structures Related to Right Duo Factor Rings

Hongying Chen, Yang Lee, Zhelin Piao∗

Department of Mathematics, Pusan National University, Pusan 46241, Korea
e-mail : 1058695917@qq.com

Department of Mathematics, Yanbian University, Yanji 133002, China and Institute of Basic Science, Daejin University, Pocheon 11159, Korea
e-mail : ylee@pusan.ac.kr

Department of Mathematics, Yanbian University, Yanji 133002, China
e-mail : zlpiao@ybu.edu.cn

Received: December 9, 2019; Revised: June 30, 2020; Accepted: June 4, 2020

### Abstract

We study the structure of rings whose factor rings modulo nonzero proper ideals are right duo; such rings are called right FD. We first see that this new ring property is not left-right symmetric. We prove for a non-prime right FD ring R that R is a subdirect product of subdirectly irreducible right FD rings; and that $R/N*(R)$ is a subdirect product of right duo domains, and $R/J(R)$ is a subdirect product of division rings, where $N*(R)$ (J(R)) is the prime (Jacobson) radical of R. We study the relation among right FD rings, division rings, commutative rings, right duo rings and simple rings, in relation to matrix rings, polynomial rings and direct products. We prove that if a ring R is right FD and $0≠e2=e∈R$ then eRe is also right FD, examining that the class of right FD rings is not closed under subrings.

Keywords: right FD ring, right duo ring, division ring, commutative ring, simple ring, non-prime right FD ring, matrix ring, polynomial ring, subring, idempotent