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Izv. Saratov Univ. Math. Mech. Inform., 2018, Volume 18, Issue 2, Pages 128–143 (Mi isu750)  

Scientific Part
Mathematics

To Chang theorem. III

S. Yu. Antonov, A. V. Antonova

Kazan State Power Engineering University, 51, Krasnoselskaya Str., Kazan, 420066, Russia

Abstract: Various multilinear polynomials of Capelli type belonging to a free associative algebra $F\{X\cup Y\}$ over an arbitrary field $F$ generated by a countable set $X \cup Y$ are considered. The formulas expressing coefficients of polynomial Chang ${\mathcal R}(\bar x, \bar y \vert \bar w)$ are found. It is proved that if the characteristic of field $F$ is not equal two then polynomial ${\mathcal R}(\bar x, \bar y \vert \bar w)$ may be represented by different ways in the form of sum of two consequences of standard polynomial $S^-(\bar x)$. The decomposition of Chang polynomial ${\mathcal H}(\bar x, \bar y \vert \bar w)$ different from already known is given. Besides, the connection between polynomials ${\mathcal R}(\bar x, \bar y \vert \bar w)$ and ${\mathcal H}(\bar x, \bar y \vert \bar w)$ is found. Some consequences of standard polynomial being of great interest for algebras with polynomial identities are obtained. In particular, a new identity of minimal degree for odd component of $Z_2$-graded matrix algebra $M^{(m,m)}(F)$ is given.

Key words: $T$-ideal, standard polynomial, Capelli polynomial.

DOI: https://doi.org/10.18500/1816-9791-2018-18-2-128-143

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Bibliographic databases:

UDC: 512

Citation: S. Yu. Antonov, A. V. Antonova, “To Chang theorem. III”, Izv. Saratov Univ. Math. Mech. Inform., 18:2 (2018), 128–143

Citation in format AMSBIB
\Bibitem{AntAnt18}
\by S.~Yu.~Antonov, A.~V.~Antonova
\paper To Chang theorem. III
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2018
\vol 18
\issue 2
\pages 128--143
\mathnet{http://mi.mathnet.ru/isu750}
\crossref{https://doi.org/10.18500/1816-9791-2018-18-2-128-143}
\elib{https://elibrary.ru/item.asp?id=35085044}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers
    • To Chang theorem
      S. Yu. Antonov, A. V. Antonova
      Izv. Saratov Univ. Math. Mech. Inform., 2015, 15:3, 247–251
    • To Chang theorem. II
      S. Yu. Antonov, A. V. Antonova
      Izv. Saratov Univ. Math. Mech. Inform., 2017, 17:2, 127–137
    • To Chang theorem. III
      S. Yu. Antonov, A. V. Antonova
      Izv. Saratov Univ. Math. Mech. Inform., 2018, 18:2, 128–143
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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