Geodesic
Theory of complete orthogonal direct decompositions of vector spaces
Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 11-49

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A theory is constructed for the complete orthogonal (with respect to generalized orthogonalities defined by certain partial symmetric bilinear functions) direct decompositions of vector spaces $V$ such that the quotient of $V$ by a certain particular subspace is finite-dimensional. The main result of the theory is a description of all such decompositions. This theory has an application to the theory of direct decompositions of $p$-ary functions, where $p$ is a prime.
Keywords: vector space, orthogonality, partial symmetric bilinear function, complete decomposition, Abelian group. 
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     author = {M. I. Anokhin},
     title = {Theory of complete orthogonal direct decompositions of vector spaces},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {11--49},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_1_a1/}
}
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M. I. Anokhin. Theory of complete orthogonal direct decompositions of vector spaces. Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 11-49. http://geodesic.mathdoc.fr/item/PDM_2012_1_a1/