Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON INTEGRAL DOMAINS IN WHICH EVERY ASCENDING CHAIN ON PRINCIPAL IDEALS IS S-STATIONARY

  • Hamed, Ahmed (Department of Mathematics Faculty of Sciences University of Monastir) ;
  • Kim, Hwankoo (Department of Information Security Hoseo University)
  • Received : 2019.10.10
  • Accepted : 2020.04.23
  • Published : 2020.09.30
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Abstract

Let D be an integral domain and S a multiplicative subset of D. An ascending chain (Ik)k∈ℕ of ideals of D is said to be S-stationary if there exist a positive integer n and an s ∈ S such that for each k ≥ n, sIk ⊆ In. As a generalization of domains satisfying ACCP (resp., ACC on ∗-ideals) we define D to satisfy S-ACCP (resp., S-ACC on ∗-ideals) if every ascending chain of principal ideals (resp., ∗-ideals) of D is S-stationary. One of main results of this paper is the Hilbert basis theorem for an integral domain satisfying S-ACCP. Also we investigate the class of such domains D and we generalize some known related results in the literature. Finally some illustrative examples regarding the introduced concepts are given.

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References

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