• Title, Summary, Keyword: *-locally factorial Krull domain

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INTEGRAL DOMAINS WITH A FREE SEMIGROUP OF *-INVERTIBLE INTEGRAL *-IDEALS

  • Chang, Gyu-Whan;Kim, Hwan-Koo
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.6
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    • pp.1207-1218
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    • 2011
  • 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.