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Matematicheskie Zametki, 1970, Volume 7, Issue 3, Pages 349–358
(Mi mzm9516)
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A ring of quotients
L. Sh. Ioffe Moscow Engineering Institute of Railroad Transportation
Abstract:
Let $\Sigma$ be a radical filter in a ring $R$, and let the ring $Q$ be defined by the equation $Q=\mathrm{Hom}_H(E, E)$, where $H=\mathrm{Hom}_R(E, E)$ and $E$ is the $\Sigma$-envelope of the ring. We show that the ring $Q$ possesses the properties of a ring of quotients and coincides with the ring of quotients in the sense of Gabriel and Bourbaki if the annihilator of any ideal $I\in\Sigma$ is equal to zero.
Received: 16.10.1968
Citation:
L. Sh. Ioffe, “A ring of quotients”, Mat. Zametki, 7:3 (1970), 349–358; Math. Notes, 7:3 (1970), 209–214
Linking options:
https://www.mathnet.ru/eng/mzm9516 https://www.mathnet.ru/eng/mzm/v7/i3/p349
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Abstract page: | 137 | Full-text PDF : | 66 | First page: | 1 |
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