Bulletin of the Korean Mathematical Society (대한수학회보)

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ON PSEUDO 2-PRIME IDEALS AND ALMOST VALUATION DOMAINS

  • Koc, Suat (Department of Mathematics Marmara University)
  • Received : 2020.07.17
  • Accepted : 2021.01.15
  • Published : 2021.07.31
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Abstract

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy ∈ P for some x, y ∈ R, then x2n ∈ Pn or y2n ∈ Pn for some n ∈ ℕ. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).

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Acknowledgement

The author would like to thank the referees for careful reading and valuable suggestions to improve the paper.

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