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The dimension of the tensor algebra of a projective bimodule

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Abstract

It is proved that the dimension of the tensor algebra of a bimodule which is projective with one of the sides differs from the dimension of the ring over which this bimodule is considered by not more than one. A criterion for these dimensions to coincide is given.

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Literature cited

  1. G. Hochschild, “Note on relative homological dimension,” Nagoya Math. J.,13, 89–94 (1958).

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  2. H. Cartan and S. Eilenberg, Homological Algebra, Princeton University Press (1956).

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Authors and Affiliations

  1. Kiev State University, USSR

    Yu. V. Roganov

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  1. Yu. V. Roganov
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Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 895–902, December, 1975.

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Roganov, Y.V. The dimension of the tensor algebra of a projective bimodule. Mathematical Notes of the Academy of Sciences of the USSR 18, 1119–1123 (1975). https://doi.org/10.1007/BF01099993

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  • DOI: https://doi.org/10.1007/BF01099993

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