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Sbornik: Mathematics, 2009, Volume 200, Issue 12, Pages 1767–1787
DOI: https://doi.org/10.1070/SM2009v200n12ABEH004058 (Mi sm7531) 		 
This article is cited in 20 scientific papers (total in 20 papers)

Upper bound for the length of commutative algebras

O. V. Markova

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (325 kB) Citations (20)
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DOI: https://doi.org/10.1070/SM2009v200n12ABEH004058
Abstract: By the length of a finite system of generators for a finite-dimensional associative algebra over an arbitrary field one means the least positive integer $k$ such that the words of length not exceeding $k$ span this algebra (as a vector space). The maximum length for the systems of generators of an algebra is referred to as the length of the algebra. In the present paper, an upper bound for the length of a commutative algebra in terms of a function of two invariants of the algebra, the dimension and the maximal degree of the minimal polynomial for the elements of the algebra, is obtained. As a corollary, a formula for the length of the algebra of diagonal matrices over an arbitrary field is obtained.
Bibliography: 8 titles.
Keywords: length of an algebra, matrix theory, commutative algebra, algebra of diagonal matrices.
Received: 28.01.2009
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 12, Pages 41–62
DOI: https://doi.org/10.4213/sm7531
Bibliographic databases:
UDC: 512.552
MSC: Primary 16P10; Secondary 16R20
Language: English
Original paper language: Russian
Citation: O. V. Markova, “Upper bound for the length of commutative algebras”, Mat. Sb., 200:12 (2009), 41–62; Sb. Math., 200:12 (2009), 1767–1787
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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