[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b190094

MORE ON THE 2-PRIME IDEALS OF COMMUTATIVE RINGS

Nikandish, Reza (Department of Mathematics Jundi-Shapur University of Technology)
Nikmehr, Mohammad Javad (Faculty of Mathematics K.N. Toosi University of Technology)
Yassine, Ali (Faculty of Mathematics K.N. Toosi University of Technology)

Publication Information

Bulletin of the Korean Mathematical Society / v.57, no.1, 2020 , pp. 117-126 More about this Journal

Abstract

Let R be a commutative ring with identity. A proper ideal I of R is called 2-prime if for all a, b ∈ R such that ab ∈ I, then either a² or b² lies in I. In this paper, we study 2-prime ideals which are generalization of prime ideals. Our study provides an analogous to the prime avoidance theorem and some applications of this theorem. Also, it is shown that if R is a PID, then the families of primary ideals and 2-prime ideals of R are identical. Moreover, a number of examples concerning 2-prime ideals are given. Finally, rings in which every 2-prime ideal is a prime ideal are investigated.

Keywords

2-prime ideal; 2-prime avoidance theorem; 2-P ring;

Citations & Related Records

Reference

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