Bavula, V.V. (2019) Left localizable rings and their characterizations. Journal of Pure and Applied Algebra, 223 (3). pp. 998-1013. ISSN 0022-4049
Abstract
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 (e.g., this is the case if a ring has a left Noetherian 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Published by Elsevier B.V. |
Keywords: | math.RA; math.RA; math.QA; 16U20, 16P50, 16S85 |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 01 Dec 2017 15:08 |
Last Modified: | 15 Jul 2020 16:22 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jpaa.2018.05.011 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:124647 |