Geodesic
Homogeneous orthogonal decompositions of commutative algebras and Hadamard matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1107-1110

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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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     author = {D. N. Ivanov},
     title = {Homogeneous orthogonal decompositions of commutative algebras and {Hadamard} matrices},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a20/}
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D. N. Ivanov. Homogeneous orthogonal decompositions of commutative algebras and Hadamard matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 4, pp. 1107-1110. http://geodesic.mathdoc.fr/item/FPM_1995_1_4_a20/