|
|
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.
 Full text:
PDF file (311 kB)
References:
PDF file
HTML file
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
\Bibitem{Ery16}
\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}
Linking options:
http://mi.mathnet.ru/eng/ivm9110 http://mi.mathnet.ru/eng/ivm/y2016/i5/p22
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:
-
M. S. Eryashkin, “Invariants of the action of a semisimple Hopf algebra on PI-algebra”, Russian Math. (Iz. VUZ), 60:8 (2016), 17–28
 -
S. Skryabin, “The left and right dimensions of a skew field over the subfield of invariants”, J. Algebra, 482 (2017), 248–263
  -
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
|
| Number of views: |
| This page: | 79 | | Full text: | 17 | | References: | 36 | | First page: | 32 |
|
Terms of Use