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Mathematics of the USSR-Sbornik, 1971, Volume 13, Issue 2, Pages 247–265
DOI: https://doi.org/10.1070/SM1971v013n02ABEH001036
(Mi sm3064)
 

This article is cited in 6 scientific papers (total in 6 papers)

Primitive $m$-near-rings over multioperator groups

S. V. Polin
References:
Abstract: In this article we examine $m\Omega$-near-rings, i.e. $(m+1)$-ary associative ringoids over $\Omega$-groups with one supplementary condition. The concept of a module over an $m\Omega$-near-ring is introduced and, with its aid, the concept of a primitive $m\Omega$-near-ring is introduced, generalizing the idea of a primitive ring. Density theorems are proved for such $m\Omega$-near-rings. With the aid of these theorems, primitive $m\Omega$-near-rings with minimum condition for right ideals are described, and a series of theorems are proved concerning the structure of $m\Omega$-near-rings, which are analogous to simple rings with minimal one-sided ideals.
Bibliography: 9 titles.
Received: 22.12.1969
Bibliographic databases:
UDC: 519.48
MSC: Primary 16A78; Secondary 08A25
Language: English
Original paper language: Russian
Citation: S. V. Polin, “Primitive $m$-near-rings over multioperator groups”, Math. USSR-Sb., 13:2 (1971), 247–265
Citation in format AMSBIB
\Bibitem{Pol71}
\by S.~V.~Polin
\paper Primitive $m$-near-rings over multioperator groups
\jour Math. USSR-Sb.
\yr 1971
\vol 13
\issue 2
\pages 247--265
\mathnet{http://mi.mathnet.ru//eng/sm3064}
\crossref{https://doi.org/10.1070/SM1971v013n02ABEH001036}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=281676}
\zmath{https://zbmath.org/?q=an:0251.08002}
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  • https://doi.org/10.1070/SM1971v013n02ABEH001036
  • https://www.mathnet.ru/eng/sm/v126/i2/p254
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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