Abstract
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.
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Presented by Kenneth Goodearl.
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Bavula, V.V. Criteria for a Ring to have aLeft Noetherian Largest Left Quotient Ring. Algebr Represent Theor 21, 359–373 (2018). https://doi.org/10.1007/s10468-017-9717-9
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DOI: https://doi.org/10.1007/s10468-017-9717-9
Keywords
- 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