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http://dx.doi.org/10.7858/eamj.2021.004

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)

Publication Information

East Asian mathematical journal / v.37, no.1, 2021 , pp. 33-40 More about this Journal

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.

Keywords

insertion property by an essential ideal; IEIP ring; IFP ring; matrix ring; Abelian ring;

Citations & Related Records

Reference

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