Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Erhard Aichinger

doi:10.1016/j.exmath.2024.125627

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Erhard Aichinger

Institute for Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

We provide a self-contained introduction to Gröbner bases of submodules of R[x1,…,xn]k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].

Original language	English
Article number	125627
Pages (from-to)	125627
Number of pages	28
Journal	Expositiones Mathematicae
Volume	42
Issue number	6
DOIs	https://doi.org/10.1016/j.exmath.2024.125627
Publication status	Published - Dec 2024

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101013 Mathematical logic
102031 Theoretical computer science

JKU Focus areas

Digital Transformation

Access to Document

10.1016/j.exmath.2024.125627

Cite this

@article{0a428c18ec2642feb7749c0e486073a9,

title = "Strong Gr{\"o}bner bases and linear algebra in multivariate polynomial rings over Euclidean domains",

abstract = "We provide a self-contained introduction to Gr{\"o}bner bases of submodules of R[x1,…,xn]k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].",

author = "Erhard Aichinger",

year = "2024",

month = dec,

doi = "10.1016/j.exmath.2024.125627",

language = "English",

volume = "42",

pages = "125627",

journal = "Expositiones Mathematicae",

issn = "0723-0869",

number = "6",

}

TY - JOUR

T1 - Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

AU - Aichinger, Erhard

PY - 2024/12

Y1 - 2024/12

N2 - We provide a self-contained introduction to Gröbner bases of submodules of R[x1,…,xn]k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].

AB - We provide a self-contained introduction to Gröbner bases of submodules of R[x1,…,xn]k, where R is a Euclidean domain, and explain how to use these bases to solve linear systems over R[x1,…,xn].

UR - https://www.sciencedirect.com/science/article/pii/S072308692400094X

UR - https://www.scopus.com/pages/publications/85208168903

U2 - 10.1016/j.exmath.2024.125627

DO - 10.1016/j.exmath.2024.125627

M3 - Article

SN - 0723-0869

VL - 42

SP - 125627

JO - Expositiones Mathematicae

JF - Expositiones Mathematicae

IS - 6

M1 - 125627

ER -

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Equations in universal algebra

Cite this

Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains

Abstract

Fields of science

JKU Focus areas

Access to Document

Other files and links

Projects

Equations in universal algebra

Cite this