Cancellation properties in ideal systems: A classification of $\boldsymbol{e.a.b.}$ semistar operations

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dc.creatorFontana, Marco
dc.creatorLoper, K. Alan
dc.date2009-05-02
dc.date.accessioned2026-07-07T13:11:17Z
dc.date.available2026-07-07T13:11:17Z
dc.descriptionWe give a classification of {\texttt{e.a.b.}} semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to partition the collection of all {\texttt{e.a.b.}} semistar (or star) operations, we show that there is exactly one operation of finite type in each equivalence class and that this operation has a range of nice properties. We give examples to demonstrate that the four classes of {\texttt{e.a.b.}} semistar (or star) operations we defined can all be distinct. In particular, we solve the open problem of showing that {\texttt{a.b.}} is really a stronger condition than {\texttt{e.a.b.}}
dc.identifierhttps://arxiv.org/abs/0905.0217
dc.identifierhttp://arxiv.org/abs/0905.0217
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229239
dc.subjectCommutative Algebra
dc.subjectAlgebraic Geometry
dc.subject13A15; 13G05; 13F30; 13E99
dc.titleCancellation properties in ideal systems: A classification of $\boldsymbol{e.a.b.}$ semistar operations
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