{"title":"Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains","authors":"Erhard Aichinger","doi":"10.1016/j.exmath.2024.125627","DOIUrl":null,"url":null,"abstract":"<div><div>We provide a self-contained introduction to Gröbner bases of submodules of <span><math><mrow><mi>R</mi><msup><mrow><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow></mrow><mrow><mi>k</mi></mrow></msup></mrow></math></span>, where <span><math><mi>R</mi></math></span> is a Euclidean domain, and explain how to use these bases to solve linear systems over <span><math><mrow><mi>R</mi><mrow><mo>[</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>]</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S072308692400094X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We provide a self-contained introduction to Gröbner bases of submodules of , where is a Euclidean domain, and explain how to use these bases to solve linear systems over .
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