Bavula, V.V. (2022) Localizations of a ring at localizable sets, their groups of units and saturations. Mathematics in Computer Science, 16 (1). 10. ISSN 1661-8270
Abstract
We continue to develop the most general theory of one-sided fractions started in Bavula (Localizable sets and the localization of a ring at a localizable set. arXiv:2112.13447). The aim of the paper is to introduce 10 types of saturations of a set in a ring and using them to study localizations of a ring at localizable sets, their groups of units and various maximal localizable sets satisfying some natural conditions. The results are obtained for denominator sets (the classical situation), Ore sets and localizable sets.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Localizable set; Localization of a ring at a localizable set; Denominator set; Localization; Left ore set; Localization at a left ore set; The group of units; Saturation |
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) |
Funding Information: | Funder Grant number The Royal Society IEC\NSFC\181444 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 May 2022 10:40 |
Last Modified: | 17 May 2022 10:40 |
Status: | Published |
Publisher: | Springer Nature |
Refereed: | Yes |
Identification Number: | 10.1007/s11786-022-00527-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:186880 |