Left localizable rings and their characterizations
Abstract
A new class of rings, the class of left localizable rings, is introduced. A ring is left localizable if each nonzero element of is invertible in some left localization of the ring . 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.
Cite
@article{arxiv.1405.4552,
title = {Left localizable rings and their characterizations},
author = {V. V. Bavula},
journal= {arXiv preprint arXiv:1405.4552},
year = {2014}
}
Comments
15 pages. arXiv admin note: text overlap with arXiv:1303.0859, arXiv:1405.0214