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Local--Global Properties for Semistar Operations

Marco Fontana·Pascual Jara·Eva Santos
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Abstract

We study the "local" behavior of several relevant properties concerning semistar operations, like finite type, stable, spectral, e.a.b. and a.b. We deal with the "global" problem of building a new semistar operation on a given integral domain, by "gluing" a given homogeneous family of semistar operations defined on a set of localizations. We apply these results for studying the local--global behavior of the semistar Nagata ring and the semistar Kronecker function ring. We prove that an integral domain $D$ is a Pr{ü}fer $\star$--multiplication domain if and only if all its localizations $D_{P}$ are Pr{ü}fer $\star_P$--multiplication domains.

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Marco Fontana, Pascual Jara, Eva Santos. 2003-05-14. Local--Global Properties for Semistar Operations. https://arxiv.org/abs/math/0305202

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