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

  • 투고 : 2010.07.04
  • 발행 : 2011.11.30

초록

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.

과제정보

연구 과제 주관 기관 : University of Incheon, National Research Foundation of Korea(NRF)

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