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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 3, Pages 332–343 (Mi jsfu191)  

This article is cited in 1 scientific paper (total in 1 paper)

Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$

Maxim N. Davletshin

Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia

Abstract: Let $K$ be a local ring of the main ideal with a nilpotent maximal ideal $J$. The paper is devoted to finished of solution of problem enumeration of ideals of the ring $K$ of $n\times n$ matrices with coefficients of $J$ on the main diagonal and above it.

Keywords: combinatorial identities, method of coefficients, enumeration of lattice, ring theory.

Full text: PDF file (200 kB)
References: PDF file   HTML file
UDC: 519.44+519.1
Received: 18.12.2010
Received in revised form: 25.02.2011
Accepted: 10.03.2011

Citation: Maxim N. Davletshin, “Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$”, J. Sib. Fed. Univ. Math. Phys., 4:3 (2011), 332–343

Citation in format AMSBIB
\Bibitem{Dav11}
\by Maxim~N.~Davletshin
\paper Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 3
\pages 332--343
\mathnet{http://mi.mathnet.ru/jsfu191}
\elib{http://elibrary.ru/item.asp?id=16446721}


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    This publication is cited in the following articles:
    1. Egorychev G.P., Kuzucuoglu F., Levchuk V.M., “Enumeration of Ideals of Some Nilpotent Matrix Rings”, J. Algebra. Appl., 12:1 (2013), 1250140  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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