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Mat. Zametki, 2012, Volume 92, Issue 2, Pages 192–201 (Mi mz8962)  

On a Matrix Nilpotent Filter

A. B. Verevkin

Ulyanovsk State University

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

DOI: https://doi.org/10.4213/mzm8962

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English version:
Mathematical Notes, 2012, 92:2, 176–185

Bibliographic databases:

Document Type: Article
UDC: 512.714
Received: 09.12.2010
Revised: 19.05.2010

Citation: A. B. Verevkin, “On a Matrix Nilpotent Filter”, Mat. Zametki, 92:2 (2012), 192–201; Math. Notes, 92:2 (2012), 176–185

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