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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)
  • Received : 2020.05.25
  • Accepted : 2020.11.02
  • Published : 2021.01.31

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

References

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