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Fundam. Prikl. Mat., 1995, Volume 1, Issue 4, Pages 1107–1110 (Mi fpm113)  

This article is cited in 7 scientific papers (total in 7 papers)

Short communications

Homogeneous orthogonal decompositions of commutative algebras and Hadamard matrices

D. N. Ivanov

Tver State University

Abstract: It is shown that a commutative algebra is a free module over every its subalgebra of the family forming its homogeneous orthogonal decomposition. As a corollary the equivalence of notions of a Hadamard matrix and an orthogonal decomposition of a commutative algebra into the sum of two-dimensional subalgebras is deduced.

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Bibliographic databases:
UDC: 512.81
Received: 01.01.1995

Citation: D. N. Ivanov, “Homogeneous orthogonal decompositions of commutative algebras and Hadamard matrices”, Fundam. Prikl. Mat., 1:4 (1995), 1107–1110

Citation in format AMSBIB
\Bibitem{Iva95}
\by D.~N.~Ivanov
\paper Homogeneous orthogonal decompositions of commutative algebras and Hadamard matrices
\jour Fundam. Prikl. Mat.
\yr 1995
\vol 1
\issue 4
\pages 1107--1110
\mathnet{http://mi.mathnet.ru/fpm113}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1791795}
\zmath{https://zbmath.org/?q=an:0868.16013}


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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. A. O. Ivanov, A. A. Tuzhilin, “The geometry of plane linear trees”, Russian Math. Surveys, 51:2 (1996), 329–330  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. D. N. Ivanov, “Orthogonal decompositions of associative algebras, and balanced systems of idempotents”, Sb. Math., 189:12 (1998), 1819–1838  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Ivanov, DN, “Orthogonal decompositions and idempotent configurations in semisimple associative algebras”, Communications in Algebra, 29:9 (2001), 3839  crossref  mathscinet  zmath  isi
    4. D. N. Ivanov, “Hadamard Algebras”, Math. Notes, 96:2 (2014), 199–203  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. D. N. Ivanov, “Degrees of Irreducible Characters and Dimensions of Hadamard Algebras”, Math. Notes, 98:2 (2015), 258–264  mathnet  crossref  crossref  mathscinet  isi  elib
    6. D. N. Ivanov, “Irreducible Characters of Hadamard Algebras”, Math. Notes, 99:6 (2016), 879–885  mathnet  crossref  crossref  mathscinet  isi  elib
    7. D. N. Ivanov, “Hadamard Decompositions of Nearly Commutative Algebras”, Math. Notes, 103:4 (2018), 583–588  mathnet  crossref  crossref  isi  elib
  • Фундаментальная и прикладная математика
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