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Mat. Zametki, 2015, Volume 98, Issue 5, Pages 747–755 (Mi mz10709)  

This article is cited in 3 scientific papers (total in 3 papers)

Just Infinite Alternative Algebras

A. S. Panasenkoab

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

Abstract: Alternative just infinite-dimensional algebras are studied, i.e., infinite-dimensional algebras in which every nonzero ideal has finite codimension. It is proved that these algebras are prime. In the nonassociative case, the Noetherian property with respect to one-sided ideals is proved, and the cases of Cayley–Dickson rings and exceptional algebras are investigated.

Keywords: alternative algebra, just infinite-dimensional algebra, prime algebra, Noetherian property with respect to one-sided ideals, Cayley–Dickson ring, exceptional algebra.

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


DOI: https://doi.org/10.4213/mzm10709

Full text: PDF file (442 kB)
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English version:
Mathematical Notes, 2015, 98:5, 805–812

Bibliographic databases:

UDC: 512.554.5
MSC: 17D05
Received: 06.03.2015

Citation: A. S. Panasenko, “Just Infinite Alternative Algebras”, Mat. Zametki, 98:5 (2015), 747–755; Math. Notes, 98:5 (2015), 805–812

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. N. Zhelyabin, A. S. Panasenko, “Nil Ideals of Finite Codimension in Alternative Noetherian Algebras”, Math. Notes, 101:3 (2017), 460–466  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. N. Zhelyabin, A. S. Panasenko, “Konstruktsiya Khersteina dlya pochti konechnomernykh superalgebr”, Sib. elektron. matem. izv., 14 (2017), 1317–1323  mathnet  crossref
    3. V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra and Logic, 57:5 (2018), 336–352  mathnet  crossref  crossref  isi
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