East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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INSERTION PROPERTY BY ESSENTIAL IDEALS

  • Nam, Sang Bok (Department of Computer Engineering, Kyungdong University) ;
  • Seo, Yeonsook (Department of Mathematics, Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics, Dong-A University)
  • Received : 2020.12.14
  • Accepted : 2021.01.15
  • Published : 2021.01.31
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Abstract

We discuss the condition that if ab = 0 for elements a, b in a ring R then aIb = 0 for some essential ideal I of R. A ring with such condition is called IEIP. We prove that a ring R is IEIP if and only if Dn(R) is IEIP for every n ≥ 2, where Dn(R) is the ring of n by n upper triangular matrices over R whose diagonals are equal. We construct an IEIP ring that is not Abelian and show that a well-known Abelian ring is not IEIP, noting that rings with the insertion-of-factors-property are Abelian.

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References

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