Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Two Extensions of a Star Operation on D to the Polynomial Ring D[X]

  • Chang, Gyu Whan (Department of Mathematics Education, Incheon National University) ;
  • Kim, Hwankoo (Division of Computer and Information Engineering, Hoseo University)
  • Received : 2020.02.22
  • Accepted : 2020.05.30
  • Published : 2021.03.31
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Abstract

Let D be an integral domain with quotient field K, X an indeterminate over D, ∗ a star operation on D, and Cl∗ (D) be the ∗-class group of D. The ∗w-operation on D is a star operation defined by I∗w = {x ∈ K | xJ ⊆ I for a nonzero finitely generated ideal J of D with J∗ = D}. In this paper, we study two star operations {∗} and [∗] on D[X] defined by A{∗} = ∩P∈∗w-Max(D) ADP [X] and A[∗] = (∩P∈∗w-Max(D) AD[X]P[X]) ∩ AK[X]. Among other things, we show that Cl∗(D) ≅ Cl[∗](D[X]) if and only if D is integrally closed.

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References

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