I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1995, VOLUME 1, NUMBER 4, PAGES 1107-1110
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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