Algebras and Representation Theory

, Volume 21, Issue 2, pp 359–373 | Cite as

Criteria for a Ring to have aLeft Noetherian Largest Left Quotient Ring

  • V. V. Bavula
Open Access


Criteria are given for a ring to have a left Noetherian largest left quotient ring. It is proved that each such a ring has only finitely many maximal left denominator sets. An explicit description of them is given. In particular, every left Noetherian ring has only finitely many maximal left denominator sets.


Goldie’s Theorem The left quotient ring of a ring The largest left quotient ring of a ring A maximal left denominator set The left localization radical of a ring An Ore set A left denominator set The prime radical 

Mathematics Subject Classification (2010)

16P50 16P60 16P20 16U20 


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of SheffieldHicks BuildingUK

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