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arXiv · 1405.4552

Left localizable rings and their characterizations

V. V. Bavula
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Abstract

A new class of rings, the class of left localizable rings, is introduced. A ring $R$ is left localizable if each nonzero element of $R$ is invertible in some left localization $S^{-1}R$ of the ring $R$. Explicit criteria are given for a ring to be a left localizable ring provided the ring has only finitely many maximal left denominator sets (eg, this is the case if a ring has a left Artinian left quotient ring). It is proved that a ring with finitely many maximal left denominator sets is a left localizable ring iff its left quotient ring is a direct product of finitely many division rings. A characterization is given of the class of rings that are finite direct product of left localization maximal rings.

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V. V. Bavula. 2014-05-18. Left localizable rings and their characterizations. https://arxiv.org/abs/1405.4552

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