Galois structure on integral valued polynomials

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• 作者：Bahar Heidaryan^a ; ^b ; ^{b.heidaryan@modares.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; Matteo Longo^a ; ^{mlongo@math.unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Giulio Peruginelli^a ; ^{gperugin@math.unipd.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13F20 ; 11R32 ; 11S20 ; 11C08
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：198-212
• 全文大小：366 K

文摘

We characterize finite Galois extensions K   of the field of rational numbers in terms of the rings class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301901&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301901&_rdoc=1&_issn=0022314X&md5=04925a88d517d5ccd95a01900985f778" title="Click to view the MathML source">Int_Q(O_K)class="mathContainer hidden">class="mathCode">${\mathrm{Int}}_{\mathbf{Q}}({\mathcal{O}}_K)$, recently introduced by Loper and Werner, consisting of those polynomials which have coefficients in class="boldFont">Q and such that class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301901&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301901&_rdoc=1&_issn=0022314X&md5=e013c49be155df5c5c62a6681265df46" title="Click to view the MathML source">f(O_K)class="mathContainer hidden">class="mathCode">$f({\mathcal{O}}_K)$ is contained in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301901&_mathId=si3.gif&_user=111111111&_pii=S0022314X16301901&_rdoc=1&_issn=0022314X&md5=0a9db2fdf02282ef25646002899f5fe7" title="Click to view the MathML source">O_Kclass="mathContainer hidden">class="mathCode">${\mathcal{O}}_K$. We also address the problem of constructing a basis for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022314X16301901&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301901&_rdoc=1&_issn=0022314X&md5=04925a88d517d5ccd95a01900985f778" title="Click to view the MathML source">Int_Q(O_K)class="mathContainer hidden">class="mathCode">${\mathrm{Int}}_{\mathbf{Q}}({\mathcal{O}}_K)$ as a class="boldFont">Z-module.