2014/05/18 by V. V. Bavula, Bavula, V. V. · 1 citation
Mathematics · #16P50 #16S85 #16U20 #Advanced Topics in Algebra #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.QA #math.RA #msc:16P50 #msc:16S85 #msc:16U20
paper · pdf · doi:10.48550/arxiv.1405.4552
15 pages. arXiv admin note: text overlap with arXiv:1303.0859, arXiv:1405.0214
arxiv created 2014/05/18 · openalex publication_date 2014/05/18 · arxiv updated 2014/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A new class of rings, the class of left localizable rings, is introduced. A ring R is left localizable if each nonzero element of R is invertible in some left localization S-1R of the ring R. Explicit criteria are given for a ring to be a left localizable ring provided the ring has only finitely many maximal left denominator sets (eg, this is the case if a ring has a left Artinian left quotient ring). It is proved that a ring with finitely many maximal left denominator sets is a left localizable ring iff its left quotient ring is a direct product of finitely many division rings. A characterization is given of the class of rings that are finite direct product of left localization maximal rings.