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Sibirsk. Mat. Zh., 2012, Volume 53, Number 4, Pages 822–838 (Mi smj2367)  

This article is cited in 3 scientific papers (total in 3 papers)

Martindale rings and $H$-module algebras with invariant characteristic polynomials

M. S. Eryashkin

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan

Abstract: Under study is the category $\mathscr A$ 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 $\widetilde{\mathscr A}$ of $\mathscr A$ such that the algebras in $\widetilde{\mathscr A}$ are integral over its subalgebras of invariants and construct a functor $\mathscr A\to\widetilde{\mathscr A}$, which is left adjoined to the inclusion $\widetilde{\mathscr A}\to\mathscr A$.

Keywords: Hopf algebras, invariant theory, Martindale ring of quotients.

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English version:
Siberian Mathematical Journal, 2012, 53:4, 659–671

Bibliographic databases:

UDC: 512.667.7
Received: 15.07.2011

Citation: M. S. Eryashkin, “Martindale rings and $H$-module algebras with invariant characteristic polynomials”, Sibirsk. Mat. Zh., 53:4 (2012), 822–838; Siberian Math. J., 53:4 (2012), 659–671

Citation in format AMSBIB
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\by M.~S.~Eryashkin
\paper Martindale rings and $H$-module algebras with invariant characteristic polynomials
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 4
\pages 822--838
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\transl
\jour Siberian Math. J.
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\vol 53
\issue 4
\pages 659--671
\crossref{https://doi.org/10.1134/S003744661204009X}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Etingof P., “Galois Bimodules and Integrality of Pi Comodule Algebras Over Invariants”, J. Noncommutative Geom., 9:2 (2015), 567–602  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. S. Eryashkin, “Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a polynomial identity”, Russian Math. (Iz. VUZ), 60:5 (2016), 18–34  mathnet  crossref  isi
    3. M. S. Eryashkin, “Invariants of the action of a semisimple Hopf algebra on PI-algebra”, Russian Math. (Iz. VUZ), 60:8 (2016), 17–28  mathnet  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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