Geodesic
Structure of modules with invariant forms
Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 28-31

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It is proved that an Artinian Noetherian module over a ring with involution on which there is defined a nondegenerate antisymmetric invariant bilinear form decomposes into a direct sum of pairwise orthogonal summands, each of which is either indecomposable or a direct sum of two indecomposable modules. This theorem had been previously proved for such modules with unique division by 2. 
@article{ZNSL_1982_114_a2,
     author = {E. A. Blagoveshchenskaya and A. V. Yakovlev},
     title = {Structure of modules with invariant forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {114},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a2/}
}
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E. A. Blagoveshchenskaya; A. V. Yakovlev. Structure of modules with invariant forms. Zapiski Nauchnykh Seminarov POMI, Modules and algebraic groups, Tome 114 (1982), pp. 28-31. http://geodesic.mathdoc.fr/item/ZNSL_1982_114_a2/