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Izv. RAN. Ser. Mat., 2010, Volume 74, Issue 1, Pages 3–134 (Mi izv1122)  

This article is cited in 10 scientific papers (total in 10 papers)

The local finite basis property and local representability of varieties of associative rings

A. Ya. Belovab

a Moscow Institute of Open Education
b Bar-Ilan University, Ramat Gan, Israel

Abstract: We prove the local representability and local finite basis property of varieties of associative rings and algebras over an arbitrary associative-commutative Noetherian ring $\Phi$.

Keywords: $\mathrm{PI}$-algebra, representable algebra, universal algebra, polynomial identity, Hilbert series, Specht problem, non-commutative algebraic geometry, representation theory, quiver.

DOI: https://doi.org/10.4213/im1122

Full text: PDF file (1540 kB)
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English version:
Izvestiya: Mathematics, 2010, 74:1, 1–126

Bibliographic databases:

UDC: 512.552.4+512.554.32+512.664.2
MSC: 16R10, 15A75, 16G20, 16P90, 16R50, 16W55, 17A30
Received: 26.06.2006

Citation: A. Ya. Belov, “The local finite basis property and local representability of varieties of associative rings”, Izv. RAN. Ser. Mat., 74:1 (2010), 3–134; Izv. Math., 74:1 (2010), 1–126

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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. Gonçalves D.J., Krasilnikov A., Sviridova I., “Limit $T$-subspaces and the central polynomials in $n$ variables of the Grassmann algebra”, J. Algebra, 371 (2012), 156–174  crossref  mathscinet  zmath  isi  scopus
    2. Belov-Kanel A., Rowen L.H., Vishne U., “Full quivers of representations of algebras”, Trans. Amer. Math. Soc., 364:10 (2012), 5525–5569  crossref  mathscinet  zmath  isi  elib  scopus
    3. I. M. Isaev, A. V. Kislitsin, “Example of simple finite dimensional algebra with no finite basis of its identities”, Comm. Algebra, 41:12 (2013), 4593–4601  crossref  mathscinet  zmath  isi
    4. Belov-Kanel A., Rowen L.H., Vishne U., “PI-varieties associated to full quivers of representations of algebras”, Trans. Am. Math. Soc., 365:5 (2013), 2681–2722  crossref  mathscinet  zmath  isi  elib  scopus
    5. G. S. Deryabina, A. N. Krasilnikov, “A Non-Finitely-Based Variety of Centrally Metabelian Pointed Groups”, Math. Notes, 95:5 (2014), 743–746  mathnet  crossref  crossref  mathscinet  isi  elib
    6. D. J. Gonçalves, A. Krasilnikov, I. Sviridova, “Limit $T$-subalgebras in free associative algebras”, J. Algebra, 412 (2014), 264–280  crossref  mathscinet  zmath  isi  scopus
    7. G. Deryabina, A. Krasilnikov, “The subalgebra of graded central polynomials of an associative algebra”, J. Algebra, 425 (2015), 313–323  crossref  mathscinet  zmath  isi  scopus
    8. A. V. Kislitsin, “An example of a central simple commutative finite-dimensional algebra with an infinite basis of identities”, Algebra and Logic, 54:3 (2015), 204–210  mathnet  crossref  crossref  mathscinet  isi
    9. A. Belov-Kanel, L. Rowen, U. Vishne, “Specht's problem for associative affine algebras over commutative Noetherian rings”, Trans. Amer. Math. Soc., 367:8 (2015), 5553–5596  crossref  mathscinet  zmath  isi  scopus
    10. A. V. Kislitsin, “Simple finite-dimensional algebras without finite basis of identities”, Siberian Math. J., 58:3 (2017), 461–466  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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