Geodesic
Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a~polynomial identity
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 22-40

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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. 
@article{IVM_2016_5_a1,
     author = {M. S. Eryashkin},
     title = {Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a~polynomial identity},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {22--40},
     publisher = {mathdoc},
     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_5_a1/}
}
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M. S. Eryashkin. Invariants and rings of quotients of $H$-semiprime $H$-module algebra satisfying a~polynomial identity. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2016), pp. 22-40. http://geodesic.mathdoc.fr/item/IVM_2016_5_a1/