Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MORE ON THE 2-PRIME IDEALS OF COMMUTATIVE RINGS

  • Received : 2019.01.26
  • Accepted : 2019.06.26
  • Published : 2020.01.31
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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.

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Acknowledgement

The authors express their deep gratitude to the referee for his/her meticulous reading and valuable suggestions which have definitely improved the paper.

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