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Further results on equivalence of multivariate polynomial matrices

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arxiv 2406.16599 v1 pith:IUKEUPH7 submitted 2024-06-24 math.AC

Jiancheng Guan , Jinwang Liu , Dongmei Li , Tao Wu This is my paper
classification math.AC
keywords matricespolynomialequivalencegeneralizedglobal-localmultivariatetheoremdeterminant
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This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. We first generalized a global-local theorem of Vaserstein. Then we proved these matrices are equivalent to their Smith forms by the generalized global-local theorem.

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  1. Smith Form Equivalence for Several Classes of Multivariate Polynomial Matrices

    math.AC 2026-04 unverdicted novelty 5.0 of 10

    Criteria for Smith form equivalence of several classes of multivariate polynomial matrices are derived via algebra isomorphisms and extended to non-square and rank-deficient cases using the Quillen-Suslin and Lin-Bose...

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