Annihilating property of zero-divisors
Commun. Korean Math. Soc. 2021 Vol. 36, No. 1, 27-39
Published online December 17, 2020
Printed January 31, 2021
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.
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