Criteria for a Ring to have aLeft Noetherian Largest Left Quotient Ring
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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.
KeywordsGoldie’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
- 6.Bavula, V.V.: Criteria for a ring to have a left Noetherian left quotient ring. arXiv:math.RA.1508.03798
- 9.Jategaonkar, A.V.: Localization in noetherian rings. Londom Mathematics Society. LMS 98, Cambridge University Press, J. Pure Appl. Alg., to appear (1986)Google Scholar
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