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Martindale rings and H-module algebras with invariant characteristic polynomials

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Abstract

Under study is the category of the possibly noncommutative H-module algebras that are mapped homomorphically onto commutative algebras. The H-equivariant Martindale ring of quotients Q H (A) is shown to be a finite-dimensional Frobenius algebra over the subfield of invariant elements Q H (A)H and also the classical ring of quotients for A. We introduce a full subcategory of such that the algebras in are integral over its subalgebras of invariants and construct a functor → , which is left adjoined to the inclusion → .

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Authors and Affiliations

  1. Chebotarev Research Institute of Mathematics and Mechanics Kazan (Volga Region) Federal University, Kazan, Russia

    M. S. Eryashkin

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  1. M. S. Eryashkin
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Correspondence to M. S. Eryashkin.

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Original Russian Text Copyright © 2012 Eryashkin M.S.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00431), the Federal Target Program “Scientific and Educational Personnel of Innovation Russia” for 2009–2013 (State Contracts P267 and 14.740.11.1142), and a grant of the President of the Russian Federation (Grant MK-6106.2012.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 4, pp. 822–838, July–August, 2012.

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Eryashkin, M.S. Martindale rings and H-module algebras with invariant characteristic polynomials. Sib Math J 53, 659–671 (2012). https://doi.org/10.1134/S003744661204009X

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  • DOI: https://doi.org/10.1134/S003744661204009X

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