Geodesic
On a Matrix Nilpotent Filter
Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 192-201 Cet article a éte moissonné depuis la source Math-Net.Ru

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We define two families of homogeneous ideals of the algebra of polynomials generated by power entries of the general matrix and its operator invariants. We study the combinatorial characteristics of these ideals and, in greater detail, the case of second order.
Keywords: nilpotent filter, commutative polynomial algebra, $\mathbb Z$-graded quotient algebra, Gröbner basis, Hilbert series
Mots-clés : filtration, Hilbert polynomial. 
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A. B. Verevkin. On a Matrix Nilpotent Filter. Matematičeskie zametki, Tome 92 (2012) no. 2, pp. 192-201. http://geodesic.mathdoc.fr/item/MZM_2012_92_2_a2/

[1] V. A. Ufnarovskii, “Kombinatornye i asimptoticheskie metody v algebre”, Algebra – 6, Itogi nauki i tekhn. Ser. Sovrem. probl. mat. Fundam. napravleniya, 57, VINITI, M., 1990, 5–177 | MR | Zbl

[2] D. Koks, Dzh. Littl, D. O'Shi, Idealy, mnogoobraziya i algoritmy. Vvedenie v vychislitelnye aspekty algebraicheskoi geometrii i kommutativnoi algebry, Mir, M., 2000 | MR | Zbl

[3] L. M. Shifner, “O stepeni matritsy”, Matem. sb., 42:3 (1935), 385–394 | Zbl