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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 4, Pages 894–915
DOI: https://doi.org/10.17377/smzh.2017.58.416 (Mi smj2907) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Identities of metabelian alternative algebras

S. V. Pchelintsevab

a Financial University Under the Government of the Russian Federation Moscow, Russia
b Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (392 kB) Citations (4)
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DOI: https://doi.org/10.17377/smzh.2017.58.416
Abstract: We study metabelian alternative (in particular, associative) algebras over a field of characteristic 0. We construct additive bases of the free algebras of mentioned varieties, describe some centers of these algebras, compute the values of the sequence of codimensions of corresponding $T$-ideals, and find unitarily irreducible components of the decomposition of mentioned varieties into a union and their bases of identities. In particular, we find a basis of identities for the metabelian alternative Grassmann algebra. We prove that the free algebra of a variety that is generated by the metabelian alternative Grassmann algebra possesses the zero associative center.
Keywords: free algebra, metabelian algebra, center of an algebra, sequence of codimensions of a Tideal, union of varieties.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00756
The author was supported by the Russian Foundation for Basic Research (Grant 16-01-00756).
Received: 01.10.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 4, Pages 693–710
DOI: https://doi.org/10.1134/S0037446617040164
Bibliographic databases:
Document Type: Article
UDC: 512.552.5+512.572
MSC: 35R30
Language: Russian
Citation: S. V. Pchelintsev, “Identities of metabelian alternative algebras”, Sibirsk. Mat. Zh., 58:4 (2017), 894–915; Siberian Math. J., 58:4 (2017), 693–710
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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