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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.

UDC: 512.81

Received: 01.01.1995

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