Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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INTEGRAL DOMAINS WITH A FREE SEMIGROUP OF *-INVERTIBLE INTEGRAL *-IDEALS

  • Received : 2010.07.04
  • Published : 2011.11.30
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Abstract

Let * be a star-operation on an integral domain R, and let $\mathfrak{I}_*^+(R)$ be the semigroup of *-invertible integral *-ideals of R. In this article, we introduce the concept of a *-coatom, and we then characterize when $\mathfrak{I}_*^+(R)$ is a free semigroup with a set of free generators consisting of *-coatoms. In particular, we show that $\mathfrak{I}_*^+(R)$ is a free semigroup if and only if R is a Krull domain and each ${\upsilon}$-invertible ${\upsilon}$-ideal is *-invertible. As a corollary, we obtain some characterizations of *-Dedekind domains.

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References

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