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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.
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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{https://elibrary.ru/item.asp?id=16446721}
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This publication is cited in the following articles:
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Egorychev G.P., Kuzucuoglu F., Levchuk V.M., “Enumeration of Ideals of Some Nilpotent Matrix Rings”, J. Algebra. Appl., 12:1 (2013), 1250140
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