{"title":"Annihilating properties of ideals generated by coefficients of polynomials and power series","authors":"N. Kim, Yang Lee, M. Ziembowski","doi":"10.1142/s0218196722500114","DOIUrl":null,"url":null,"abstract":"In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196722500114","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text], whenever [Formula: see text] and [Formula: see text]. Next we prove that if [Formula: see text] for power series [Formula: see text] over any ring [Formula: see text], then for any [Formula: see text], there exist positive integers [Formula: see text] and [Formula: see text] such that [Formula: see text] when [Formula: see text] and [Formula: see text], [Formula: see text] for each [Formula: see text].
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