Orthogonal decompositions of associative algebras, and balanced systems of idempotents
Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1819-1838

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The divisibility conjecture for commutative orthogonal decompositions is proved. In addition, Hadamard decompositions and balanced systems of idem-potents are studied.
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     author = {D. N. Ivanov},
     title = {Orthogonal decompositions of associative algebras, and balanced systems of idempotents},
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D. N. Ivanov. Orthogonal decompositions of associative algebras, and balanced systems of idempotents. Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1819-1838. http://geodesic.mathdoc.fr/item/SM_1998_189_12_a5/