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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1970, Volume 7, Issue 3, Pages 349–358 (Mi mz9516)

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.

Full text: PDF file (1176 kB)

English version:
Mathematical Notes, 1970, 7:3, 209–214

Bibliographic databases:

UDC: 512.4

Citation: L. Sh. Ioffe, “A ring of quotients”, Mat. Zametki, 7:3 (1970), 349–358; Math. Notes, 7:3 (1970), 209–214

Citation in format AMSBIB
\Bibitem{Iof70} \by L.~Sh.~Ioffe \paper A ring of quotients \jour Mat. Zametki \yr 1970 \vol 7 \issue 3 \pages 349--358 \mathnet{http://mi.mathnet.ru/mz9516} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=260802} \zmath{https://zbmath.org/?q=an:0209.33701} \transl \jour Math. Notes \yr 1970 \vol 7 \issue 3 \pages 209--214 \crossref{https://doi.org/10.1007/BF01093117}