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Mat. Zametki, 1972, Volume 12, Issue 3, Pages 239–242 (Mi mz9873)  

The right ideals of an alternative ring

K. A. Zhevlakov

Institute of Mathematics, Siberian Division, Academy of Sciences of the USSR

Abstract: It is proved that if $P$ is a right ideal and $I$ a two-sided ideal of an alternative ring $A$, then neither $P^2$ nor $IP$ is in general a right ideal of $A$. Moreover, it is shown that in the alternative ring $A$ the right annihilator of the right ideal $P$, i.e., the set $\mathfrak{Z}_r(P)=ż\in A\mid Pz=0\}$, is not necessarily either a left or a right ideal, nor even a subring of $A$.

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English version:
Mathematical Notes, 1972, 12:3, 578–579

Bibliographic databases:

UDC: 519.48
Received: 30.03.1972

Citation: K. A. Zhevlakov, “The right ideals of an alternative ring”, Mat. Zametki, 12:3 (1972), 239–242; Math. Notes, 12:3 (1972), 578–579

Citation in format AMSBIB
\Bibitem{Zhe72}
\by K.~A.~Zhevlakov
\paper The right ideals of an alternative ring
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 3
\pages 239--242
\mathnet{http://mi.mathnet.ru/mz9873}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=321998}
\zmath{https://zbmath.org/?q=an:0272.17006}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 3
\pages 578--579
\crossref{https://doi.org/10.1007/BF01093987}


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