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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 5, Pages 22–40 (Mi ivm9110)  

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

Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a polynomial identity

M. S. Eryashkin

Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: We consider an action of a finite-dimensional Hopf algebra $H$ on a PI-algebra. We prove that an $H$-semiprime $H$-module algebra $A$ has a Frobenius artinian classical ring of quotients $Q$ if $A$ has a finite set of $H$-prime ideals with zero intersection. The ring of quotients $Q$ is an $H$-semisimple $H$-module algebra and finitely generated module over the subalgebra of central invariants. Moreover, if the algebra $A$ is projective module of constant rank over its center then $A$ is integral over the subalgebra of central invariants.

Keywords: Hopf algebras, invariant theory, PI-algebras, rings of quotients.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-31200
Ministry of Education and Science of the Russian Federation НШ-941.2014.1
1.2045.2014


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:5, 18–34

Bibliographic databases:

UDC: 512.667
Received: 30.09.2014

Citation: M. S. Eryashkin, “Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a polynomial identity”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 5, 22–40; Russian Math. (Iz. VUZ), 60:5 (2016), 18–34

Citation in format AMSBIB
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\by M.~S.~Eryashkin
\paper Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a~polynomial identity
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 5
\pages 22--40
\mathnet{http://mi.mathnet.ru/ivm9110}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 5
\pages 18--34
\crossref{https://doi.org/10.3103/S1066369X16050029}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000409282900002}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971278451}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. S. Skryabin, “The left and right dimensions of a skew field over the subfield of invariants”, J. Algebra, 482 (2017), 248–263  crossref  mathscinet  zmath  isi  scopus
    3. S. M. Skryabin, “Podkoltsa invariantov dlya deistvii konechnomernykh algebr Khopfa”, Trudy seminara kafedry algebry i matematicheskoi logiki Kazanskogo (Privolzhskogo) federalnogo universiteta, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 158, VINITI RAN, M., 2018, 40–80  mathnet  mathscinet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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