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Mat. Zametki, 2003, Volume 74, Issue 6, Pages 924–933 (Mi mz320)  

This article is cited in 1 scientific paper (total in 1 paper)

Orders in Uniserial Rings

A. A. Tuganbaev

Moscow Power Engineering Institute (Technical University)

Abstract: Let $A$ be a ring, and let $T(A)$ and $N(A)$ be the set of all the regular elements of $A$ and the set of all nonregular elements of $A$, respectively. It is proved that $A$ is a right order in a right uniserial ring if and only if the set of all regular elements of $A$ is a left ideal in the multiplicative semigroup $A$ and for any two elements $a_1$ and $a_2$ of $A$, either there exist two elements $b_1\in A$ and $t_1\in T(A)$ with $a_1b_1 = a_2t_1$ or there exist two elements $b_2\in A$ and $t_2\in T(A)$ with $a_2b_2 = a_1t_2$. A right distributive ring $A$ is a right order in a right uniserial ring if and only if the set $N(A)$ is a left ideal of $A$. If $A$ is a right distributive ring such that all its right divisors of zero are contained in the Jacobson radical $J(A)$ of $A$, then $A$ is a right order in a right uniserial ring.

DOI: https://doi.org/10.4213/mzm320

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English version:
Mathematical Notes, 2003, 74:6, 874–882

Bibliographic databases:

UDC: 512.55
Received: 28.07.2001

Citation: A. A. Tuganbaev, “Orders in Uniserial Rings”, Mat. Zametki, 74:6 (2003), 924–933; Math. Notes, 74:6 (2003), 874–882

Citation in format AMSBIB
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\by A.~A.~Tuganbaev
\paper Orders in Uniserial Rings
\jour Mat. Zametki
\yr 2003
\vol 74
\issue 6
\pages 924--933
\mathnet{http://mi.mathnet.ru/mz320}
\crossref{https://doi.org/10.4213/mzm320}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054011}
\zmath{https://zbmath.org/?q=an:1111.16005}
\transl
\jour Math. Notes
\yr 2003
\vol 74
\issue 6
\pages 874--882
\crossref{https://doi.org/10.1023/B:MATN.0000009024.45952.4a}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000187966900032}


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    This publication is cited in the following articles:
    1. Marks G., Mazurek R., “Annelidan rings”, Forum Math., 28:5 (2016), 923–941  crossref  mathscinet  zmath  isi  elib  scopus
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