2018/03/13 by Mohsen Aghajani, Abolfazl Tarizadeh, Aghajani, Mohsen +1
Mathematics · #13A99 #13B10 #13E05 #13H99 #14A05 #14A15 #14R05 #14R10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1803.04817
openalex publication_date 2018/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, new criteria for zero dimensional rings, Gelfand rings, clean\nrings and mp-rings are given. A new class of rings is introduced and studied,\nwe call them purified rings. Specially, reduced purified rings are\ncharacterized. New characterizations for pure ideals of reduced Gelfand rings\nand mp-rings are provided. It is also proved that if the topology of a scheme\nis Hausdorff, then the affine opens of that scheme is stable under taking\nfinite unions. In particular, every compact scheme is an affine scheme.\n