Abstract
It is proved that a finitely spaced module over ak-category admits a multiplicative basis (such a module gives rise to a matrix problem in which the allowed column transformations are determined by a module structure, the row transformations are arbitrary, and the number of canonical matrices is finite).
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References
R. Bautista, P. Gabriel, A. V. Roiter, and L. Salmeron, “Representations of finite algebras and multiplicative bases,”Invent. Math.,81, 217–285 (1985).
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P. Gabriel, L. A. Nazarova, A. V. Roiter, V.V. Sergeichuk, and D. Vossieck, “Tame and wild subspace problems,”Ukr. Mat. Zh.,45, No. 3, 313–352 (1993).
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 5, pp. 567–579, May, 1994.
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Roiter, A.V., Sergeichuk, V.V. Existence of a multiplicative basis for a finitely spaced module over an aggregate. Ukr Math J 46, 604–617 (1994). https://doi.org/10.1007/BF01058522
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DOI: https://doi.org/10.1007/BF01058522