Geodesic
Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 332-343

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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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     author = {Maxim N. Davletshin},
     title = {Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {332--343},
     publisher = {mathdoc},
     volume = {4},
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     year = {2011},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_3_a6/}
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Maxim N. Davletshin. Enumeration of $\mathcal D$-invariant ideals of the ring $\mathrm{R_n(K,J)}$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 332-343. http://geodesic.mathdoc.fr/item/JSFU_2011_4_3_a6/