2009/05/02 by Marco Fontana, Fontana, Marco, K. Alan Loper +1
Computer Science · Mathematics · #13A15 #13E99 #13F30 #13G05 #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A15 #msc:13E99 #msc:13F30 #msc:13G05
paper · pdf · doi:10.48550/arxiv.0905.0217
arxiv created 2009/05/02 · openalex publication_date 2009/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a classification of 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 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 e.a.b. semistar (or star) operations we defined can all be distinct. In particular, we solve the open problem of showing that a.b. is really a stronger condition than e.a.b.