2014/08/24 by V. V. Bavula, Bavula, V. V.
Mathematics · #16P50 #16S85 #16U20 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16P50 #msc:16S85 #msc:16U20
paper · pdf · doi:10.48550/arxiv.1408.5608
19 pages. arXiv admin note: substantial text overlap with arXiv:1405.4552
arxiv created 2014/08/24 · arxiv updated 2014/08/26
A new class of rings, \em the class of weakly left localizable rings, is introduced. A ring R is called \em weakly left localizable if each non-nilpotent 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 weakly 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 that satisfies some natural conditions is a weakly left localizable ring iff its left quotient ring is a direct product of finitely many local rings such that their radicals are nil ideals.