Hadamard Algebras Possessing the Unique Noncommutative Simple Component / Ivanov D.N. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. ? 5. P. 46-48 [Moscow Univ. Math. Bulletin. Vol. 66, N 5, 2011.].

The famous conjecture on the orders of Hadamard matrices can be reformulated as follows: a commutative algebra is Hadamard if and only if its dimension is divisible by 4. In this paper we study the Hadamard algebras closed to commutative ones, namely, the algebras possessing the unique noncommutative simple component being the matrix algebra of order 2.

Key words: orthogonal decompositions, Hadamard algebras, Hadamard matrices.