On the integer form of the additive Hilbert's Theorem 90

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• 作者：Zaï ; mi ; Toufik
• 关键词：11R04 ; 11R32 ; 11R21 ; Hilbert's Theorem 90 ; Number fields ; Cyclic extensions
• 刊名：Linear Algebra and its Applications
• 出版年：2004
• 出版时间：October 1, 2004
• 年：2004
• 卷：390
• 期：Complete
• 页码：175-181
• 全文大小：192 K

文摘

Let K be a number field whose ring of integers is a principal ideal domain and let E be a cyclic Galois extension of K. We prove that every integer of E with zero trace is a difference of two conjugates of an integer of E if and only if there is an integer of E with trace 1.