Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2021; 36(1): 27-39

Online first article December 17, 2020      Printed January 31, 2021

https://doi.org/10.4134/CKMS.c200176

Copyright © The Korean Mathematical Society.

Annihilating property of zero-divisors

Da Woon Jung, Chang Ik Lee, Yang Lee, Sang Bok Nam, Sung Ju Ryu, Hyo Jin Sung, Sang Jo Yun

Pusan National University; Pusan National University; Daejin University; Kyungdong University; Pusan National University; Pusan National University; Dong-A University

Abstract

We discuss the condition that every nonzero right annihilator of an element contains a nonzero ideal, as a generalization of the insertion-of-factors-property. A ring with such condition is called {\it right AP}. We prove that a ring $R$ is right AP if and only if $D_n(R)$ is right AP for every $n\geq 2$, where $D_n(R)$ is the ring of $n$ by $n$ upper triangular matrices over $R$ whose diagonals are equal. Properties of right AP rings are investigated in relation to nilradicals, prime factor rings and minimal order.

Keywords: Right AP ring, IFP ring, annihilator, matrix ring, nilradical, prime factor ring

MSC numbers: 16D25, 16U80, 16S50

Supported by: The second named author was supported by NRF-2019R1I1A3A01058630. The fourth named author was supported by Kyungdong University Research Fund, 2020.