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Diskr. Mat., 2018, Volume 30, Issue 4, Pages 41–46 (Mi dm1533)  

Centrally essential rings which are not necessarily unital or associative

V. T. Markova, A. A. Tuganbaevba

a Lomonosov Moscow State University
b National Research University "Moscow Power Engineering Institute"

Abstract: Centrally essential rings were defined earlier for associative unital rings; in this paper, we define them for rings which are not necessarily associative or unital. In this case, it is proved that centrally essential semiprime rings are commutative. It is proved that all idempotents of a centrally essential alternative ring are central. Several examples of non-commutative centrally essential rings are provided, some properties of centrally essential rings are described.

Keywords: centrally essential ring, semiprime ring, idempotent, non-unital ring, alternative ring.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00895-A
Russian Science Foundation 16-11-10013


DOI: https://doi.org/10.4213/dm1533

Full text: PDF file (136 kB)
First page: PDF file
References: PDF file   HTML file

Document Type: Article
UDC: 512.55
Received: 26.07.2018

Citation: V. T. Markov, A. A. Tuganbaev, “Centrally essential rings which are not necessarily unital or associative”, Diskr. Mat., 30:4 (2018), 41–46

Citation in format AMSBIB
\Bibitem{MarTug18}
\by V.~T.~Markov, A.~A.~Tuganbaev
\paper Centrally essential rings which are not necessarily unital or associative
\jour Diskr. Mat.
\yr 2018
\vol 30
\issue 4
\pages 41--46
\mathnet{http://mi.mathnet.ru/dm1533}
\crossref{https://doi.org/10.4213/dm1533}
\elib{http://elibrary.ru/item.asp?id=36447990}


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