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Matematicheskie Zametki, 2012, Volume 92, Issue 2, Pages 192–201
DOI: https://doi.org/10.4213/mzm8962 (Mi mzm8962) 		 
On a Matrix Nilpotent Filter

A. B. Verevkin

Ulyanovsk State University
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DOI: https://doi.org/10.4213/mzm8962
Abstract: 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, filtration, Hilbert polynomial.
Received: 09.12.2010
Revised: 19.05.2010
English version:
Mathematical Notes, 2012, Volume 92, Issue 2, Pages 176–185
DOI: https://doi.org/10.1134/S0001434612070206
Bibliographic databases:
Document Type: Article
UDC: 512.714
Language: Russian
Citation: A. B. Verevkin, “On a Matrix Nilpotent Filter”, Mat. Zametki, 92:2 (2012), 192–201; Math. Notes, 92:2 (2012), 176–185
Citation in format AMSBIB
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