Abstract
It is shown that if the Λ -Ω -bimodule M generates a category of Λ -Ω -bimodules, then the ideal of identities of the triangular extension of the direct sum of algebras Λ and Ω by means of the bimodule M is equal to the product of ideals of identities of the algebras Λ and Ω.
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Literature cited
U. É. Kal'yulaid, “A remark on the basis of identities of the algebra of upper triangular matrices,” in: Methods of Algebra and Functional Analysis for Investigating Families of Operators [in Russian], Tartu (1978), pp. 105–107.
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J. Lewin, “A matrix representation for associative algebras, I,” Trans. Am. Math. Soc.,188, No. 2, 293–308 (1974).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 132, pp. 5–11, 1983.
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Abakarov, A.S., Yakovlev, A.V. Triangular extension identities. J Math Sci 30, 1795–1799 (1985). https://doi.org/10.1007/BF02105090
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DOI: https://doi.org/10.1007/BF02105090