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Criteria for a ring to have a left Noetherian largest left quotient ring. (English) Zbl 1391.16023

Summary: 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.

MSC:

16P50 Localization and associative Noetherian rings
16P60 Chain conditions on annihilators and summands: Goldie-type conditions
16P20 Artinian rings and modules (associative rings and algebras)
16U20 Ore rings, multiplicative sets, Ore localization
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