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Mat. Zametki, 2017, Volume 101, Issue 3, Pages 395–402 (Mi mz11119)  

This article is cited in 2 scientific papers (total in 2 papers)

Nil Ideals of Finite Codimension in Alternative Noetherian Algebras

V. N. Zhelyabinab, A. S. Panasenkob

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: Alternative (right) Noetherian algebras are considered. It is proved that, in these algebras, the nil ideals of finite codimension are nilpotent, which generalizes the corresponding Zhevlakov's result. As a corollary, we describe just infinite alternative nonassociative algebras (for the field characteristic distinct from 2).

Keywords: Noetheriaty, nil ideal, alternative algebra, just infinite algebra, exceptional algebra, codimension.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00014

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11119

Full text: PDF file (432 kB)
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English version:
Mathematical Notes, 2017, 101:3, 460–466

Bibliographic databases:

UDC: 512.554.5
MSC: 17D05
Received: 18.02.2016
Revised: 31.03.2016

Citation: V. N. Zhelyabin, A. S. Panasenko, “Nil Ideals of Finite Codimension in Alternative Noetherian Algebras”, Mat. Zametki, 101:3 (2017), 395–402; Math. Notes, 101:3 (2017), 460–466

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v101/i3/p395

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Zhelyabin, A. S. Panasenko, “Konstruktsiya Khersteina dlya pochti konechnomernykh superalgebr”, Sib. elektron. matem. izv., 14 (2017), 1317–1323  mathnet  crossref
    2. V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra and Logic, 57:5 (2018), 336–352  mathnet  crossref  crossref  isi
  • Математические заметки Mathematical Notes
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