Uspekhi Matematicheskikh Nauk
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1969, Volume 24, Issue 1(145), Pages 39–42 (Mi umn5449)  

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


Series of articles on the multioperator rings and algebras
Two theorems on identities in multioperator algebras

F. I. Kizner


Abstract: Two (unconnected) propositions on $\Omega$-algebras with identical relations are proved. The first of these (Theorem 1, in § 1) generalizes to $\Omega$-algebras a known fact from the theory of associative linear algebras, which asserts that every finite-dimensional algebra is an algebra with identical relations (more exactly, every algebra $A$ of dimension over a field $m$ satisfies a so-called standard identity of degree $m+1$). In § 2 we prove that every identical relation in an $\Omega$-algebra over a field of characteristic zero is equivalent to a system of polylinear identical relations (Theorem 2), from which it follows that the study of $\Omega$-algebras with arbitrary identical relations reduces to that of $\Omega$-algebras with polylinear identical relations. This theorem is proved in practically the same way as the corresponding proposition for ordinary algebras with identical relations, that is, algebras with a single binary multiplication (see for example, Mal'tsev [1]); it is clearly a generalization of it.

Full text: PDF file (379 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1969, 24:1, 37–40

Bibliographic databases:

UDC: 519.4+519.9
MSC: 16R10, 47C05
Received: 30.09.1968

Citation: F. I. Kizner, “Two theorems on identities in multioperator algebras”, Uspekhi Mat. Nauk, 24:1(145) (1969), 39–42; Russian Math. Surveys, 24:1 (1969), 37–40

Citation in format AMSBIB
\Bibitem{Kiz69}
\by F.~I.~Kizner
\paper Two theorems on identities in multioperator algebras
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 1(145)
\pages 39--42
\mathnet{http://mi.mathnet.ru/umn5449}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=237406}
\zmath{https://zbmath.org/?q=an:0191.03202|0211.06302}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 1
\pages 37--40
\crossref{https://doi.org/10.1070/RM1969v024n01ABEH001337}


Linking options:
  • http://mi.mathnet.ru/eng/umn5449
  • http://mi.mathnet.ru/eng/umn/v24/i1/p39

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. A. G. Kurosh, “Multioperator rings and algebras”, Russian Math. Surveys, 24:1 (1969), 1–13  mathnet  crossref  mathscinet  zmath
    2. M. S. Burgin, “Commutative products of linear $\Omega$-algebras”, Math. USSR-Izv., 4:5 (1970), 979–999  mathnet  crossref  mathscinet  zmath
    3. M. S. Burgin, “Gruppoid mnogoobrazii lineinykh $\Omega$-algebr”, UMN, 25:3(153) (1970), 263–264  mathnet  mathscinet  zmath
    4. M. S. Burgin, V. A. Artamonov, “Some properties of subalgebras in varieties of linear $\Omega$-albebras”, Math. USSR-Sb., 16:1 (1972), 69–85  mathnet  crossref  mathscinet  zmath
    5. T. M. Baranovich, M. S. Burgin, “Linear $\Omega$-algebras”, Russian Math. Surveys, 30:4 (1975), 65–113  mathnet  crossref  mathscinet  zmath
    6. S. N. Tronin, “Operads and varieties of algebras defined by polylinear identities”, Siberian Math. J., 47:3 (2006), 555–573  mathnet  crossref  mathscinet  zmath  isi  elib
    7. S. N. Tronin, “Superalgebras and operads. I”, Siberian Math. J., 50:3 (2009), 503–514  mathnet  crossref  mathscinet  isi  elib  elib
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:197
    Full text:81
    References:37
    First page:1

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021