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Title: Radical of a relatively free associative algebra over fields of positive characteristic

Abstract

The following Kemer problem on the nilindex of the radical is solved: it is shown that the Jacobson radical of a relatively free associative algebra over an infinite field of positive characteristic is a nilideal of bounded index. A basis of the identities with forms for matrix algebras over infinite fields of positive characteristic is described. Bibliography: 10 titles.

Authors:
 [1]
  1. Ul'yanovsk State University, Ul'yanovsk (Russian Federation)
Publication Date:
OSTI Identifier:
21096776
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 199; Journal Issue: 5; Other Information: DOI: 10.1070/SM2008v199n05ABEH003940; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; INDEXES; MATHEMATICAL LOGIC; MATRICES

Citation Formats

Samoilov, L M. Radical of a relatively free associative algebra over fields of positive characteristic. United States: N. p., 2008. Web. doi:10.1070/SM2008V199N05ABEH003940; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Samoilov, L M. Radical of a relatively free associative algebra over fields of positive characteristic. United States. https://doi.org/10.1070/SM2008V199N05ABEH003940; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Samoilov, L M. 2008. "Radical of a relatively free associative algebra over fields of positive characteristic". United States. https://doi.org/10.1070/SM2008V199N05ABEH003940; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21096776,
title = {Radical of a relatively free associative algebra over fields of positive characteristic},
author = {Samoilov, L M},
abstractNote = {The following Kemer problem on the nilindex of the radical is solved: it is shown that the Jacobson radical of a relatively free associative algebra over an infinite field of positive characteristic is a nilideal of bounded index. A basis of the identities with forms for matrix algebras over infinite fields of positive characteristic is described. Bibliography: 10 titles.},
doi = {10.1070/SM2008V199N05ABEH003940; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
url = {https://www.osti.gov/biblio/21096776}, journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 5,
volume = 199,
place = {United States},
year = {Mon Jun 30 00:00:00 EDT 2008},
month = {Mon Jun 30 00:00:00 EDT 2008}
}