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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 79–100 (Mi izv1472)  

This article is cited in 13 scientific papers (total in 13 papers)

Prime algebras and absolute zero divisors

S. V. Pchelintsev


Abstract: This paper is devoted to the solution of the problem of absolute zero divisors in the varieties of Jordan algebras and $(-1,1)$-algebras over a field of characteristic $0$. It is shown that in those varieties there exist prime algebras generated by absolute zero divisors.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 79–98

Bibliographic databases:

UDC: 519.48
MSC: Primary 17C10, 17D20; Secondary 17D05, 17D15
Received: 21.11.1983

Citation: S. V. Pchelintsev, “Prime algebras and absolute zero divisors”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 79–100; Math. USSR-Izv., 28:1 (1987), 79–98

Citation in format AMSBIB
\Bibitem{Pch86}
\by S.~V.~Pchelintsev
\paper Prime algebras and absolute zero divisors
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 79--100
\mathnet{http://mi.mathnet.ru/izv1472}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835567}
\zmath{https://zbmath.org/?q=an:0615.17011|0609.17008}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 79--98
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000868}


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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. S. V. Pchelintsev, “On central ideals of finitely generated binary $(-1,1)$-algebras”, Sb. Math., 193:4 (2002), 585–607  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. Brešar, D. Eremita, A. R. Villena, “Functional Identities in Jordan Algebras: Associating Traces and Lie Triple Isomorphisms”, Communications in Algebra, 31:3 (2003), 1207  crossref  elib
    3. S. V. Pchelintsev, “Nilpotency of the alternator ideal of a finitely generated binary $(-1,1)$-algebra”, Siberian Math. J., 45:2 (2004), 356–375  mathnet  crossref  mathscinet  zmath  isi  elib
    4. M. Cabrera, A. R. Villena, “Multiplicative-Semiprimeness of Nondegenerate Jordan Algebras”, Communications in Algebra, 32:10 (2005), 3995  crossref
    5. S. V. Pchelintsev, “Isotopes of prime $(-1,1)$- and Jordan algebras”, Algebra and Logic, 49:3 (2010), 262–288  mathnet  crossref  mathscinet  zmath  elib  elib
    6. J. C. Cabello, M. Cabrera, R. Roura, “A note on multiplicative primeness of prime degenerate Jordan algebras”, Siberian Math. J., 51:5 (2010), 818–823  mathnet  crossref  mathscinet  isi  elib
    7. É Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. IV. Equational domains and codomains”, Algebra and Logic, 49:6 (2010), 483–508  mathnet  crossref  mathscinet  isi
    8. V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Siberian Math. J., 53:3 (2012), 450–460  mathnet  crossref  mathscinet  isi
    9. V. N. Zhelyabin, “Examples of prime Jordan superalgebras of vector type and superalgebras of Cheng–Kac type”, Siberian Math. J., 54:1 (2013), 33–39  mathnet  crossref  mathscinet  isi
    10. S. V. Pchelintsev, “Commutator identities of the homotopes of $(-1,1)$-algebras”, Siberian Math. J., 54:2 (2013), 325–340  mathnet  crossref  mathscinet  isi
    11. S. V. Pchelintsev, “Degenerate alternative algebras”, Siberian Math. J., 55:2 (2014), 323–335  mathnet  crossref  mathscinet  isi
    12. José A. Anquela, Teresa Cortés, Esther García, Miguel Gómez Lozano, “Prime Quotients of Jordan Systems and Lie Algebras”, Mediterr. J. Math, 2015  crossref
    13. S. V. Pchelintsev, “Prime algebras connected with monsters”, Siberian Math. J., 59:2 (2018), 341–356  mathnet  crossref  crossref  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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