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

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

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Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of SheffieldHicks BuildingUK

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