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.
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
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.
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