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http://dx.doi.org/10.4134/CKMS.c200176

ANNIHILATING PROPERTY OF ZERO-DIVISORS  

Jung, Da Woon (Finance.Fishery.Manufacture Industrial Mathematics Center on Big Data Pusan National University)
Lee, Chang Ik (Department of Mathematics Pusan National University)
Lee, Yang (Department of Mathematics Pusan National University)
Nam, Sang Bok (Department of Computer Engineering Kyungdong University)
Ryu, Sung Ju (Department of Mathematics Pusan National University)
Sung, Hyo Jin (Department of Mathematics Pusan National University)
Yun, Sang Jo (Department of Mathematics Dong-A University)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.1, 2021 , pp. 27-39 More about this Journal
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 right AP. We prove that a ring R is right AP if and only if Dn(R) is right AP for every n ≥ 2, where Dn(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;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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