Abstract
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.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 28–31, 1982.
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Blagoveshchenskaya, E.A., Yakovlev, A.V. Structure of modules with invariant forms. J Math Sci 27, 2848–2851 (1984). https://doi.org/10.1007/BF01410737
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DOI: https://doi.org/10.1007/BF01410737