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Izv. Akad. Nauk SSSR Ser. Mat., 1973, Volume 37, Issue 2, Pages 284–288 (Mi izv2246)  

This article is cited in 7 scientific papers (total in 7 papers)

On the dimension of noncommutative affine algebras

V. T. Markov


Abstract: Let $R$ be a finitely generated prime $PI$-algebra over a field $F$. $Z$ is the center of its ring of fractions. It is proved that $Z$ is the field of fractions of the center of $R$ and that the transcendence degree of $Z$ over $F$ is equal to the maximal length of a chain of prime ideals in $R$.

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English version:
Mathematics of the USSR-Izvestiya, 1973, 7:2, 281–285

Bibliographic databases:

UDC: 519.4
MSC: Primary 16A38, 16A08; Secondary 16A42, 16A12
Received: 16.05.1972

Citation: V. T. Markov, “On the dimension of noncommutative affine algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 37:2 (1973), 284–288; Math. USSR-Izv., 7:2 (1973), 281–285

Citation in format AMSBIB
\Bibitem{Mar73}
\by V.~T.~Markov
\paper On the dimension of noncommutative affine algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1973
\vol 37
\issue 2
\pages 284--288
\mathnet{http://mi.mathnet.ru/izv2246}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=360683}
\zmath{https://zbmath.org/?q=an:0255.16007}
\transl
\jour Math. USSR-Izv.
\yr 1973
\vol 7
\issue 2
\pages 281--285
\crossref{https://doi.org/10.1070/IM1973v007n02ABEH001936}


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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. William Schelter, “Non-commutative affine P. I. rings are catenary”, Journal of Algebra, 51:1 (1978), 12  crossref
    2. S.A Amitsur, L.W Small, “Prime ideals in PI-rings”, Journal of Algebra, 62:2 (1980), 358  crossref
    3. E. I. Zel'manov, “Lie algebras with an algebraic adjoint representation”, Math. USSR-Sb., 49:2 (1984), 537–552  mathnet  crossref  mathscinet  zmath
    4. I. P. Shestakov, “Finitely generated special Jordan and alternative $PI$-algebras”, Math. USSR-Sb., 50:1 (1985), 31–40  mathnet  crossref  mathscinet  zmath
    5. E. I. Zel'manov, “Lie algebras with a finite gradation”, Math. USSR-Sb., 52:2 (1985), 347–385  mathnet  crossref  mathscinet  zmath
    6. E. I. Zel'manov, “A solution of the restricted Burnside problem for 2-groups”, Math. USSR-Sb., 72:2 (1992), 543–565  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Youngsun Yoon, “On the polynomial representations of current algebras”, Journal of Algebra, 252:2 (2002), 376  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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