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研究生:楊佳儒
研究生(外文):YANG, JIA-RU
論文名稱:質環上的一個函數恆等式
論文名稱(外文):A functional identity in prime rings
指導教授:劉承楷
指導教授(外文):LIU, CHENG-KAI
口試委員:蔡援宗劉承楷杜子明
口試委員(外文):TSAI, YUAN-TSUNGLIU, CHENG-KAITO, TZE-MING
口試日期:2022-07-07
學位類別:碩士
校院名稱:國立彰化師範大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2022
畢業學年度:110
語文別:英文
論文頁數:21
中文關鍵詞:質環導算函數恆等式
外文關鍵詞:prime ringderivationfunctional identity
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假設R是一個特徵值不是2且不是3的質環,C是R的擴張中心,Q是R的極大右商環。本篇論文中,我們證明若兩個加性函數d:R→R與δ:R→R對所有元素x∈R 皆滿足函數恆等式d(x^3 )=d(x)x^2+xδ(x)x+x^2 d(x)時,則必會存在一個元素a∈Q、一個導算∆:R→Q與一個加性函數μ:R→C,使得對所有元素x∈R 皆滿足d(x)=∆(x)+ax+μ(x)和δ(x)=∆(x)-xa-2μ(x)。這個結果自然地推廣了質環上的喬丹三重導算、雙重圓投影、三重導算與3喬丹導算等相關的著名定理。
Let R be a prime ring of characteristic charR≠2,3, let C be the extended centroid of R and let Q be the maximal right ring of quotients of R. Suppose that d:R→R and δ:R→R are two additive maps satisfying d(x^3 )=d(x) x^2+xδ(x)x+x^2 d(x) for all x∈R. It is shown that there exist a∈Q, a derivation ∆:R→Q and an additive map μ:R→C with μ(x^3 )=0 for all x∈R such that d(x)=∆(x)+ax+μ(x) and δ(x)=∆(x)-xa-2μ(x) for all x∈R. Our result naturally generalizes several known theorems concerning Jordan triple derivations, bicircular projection mappings, triple derivations and 3-Jordan derivations on prime rings.
中文摘要 I
Abstract II
致謝 III
Contents IV

Introduction and Results 1
Preliminaries 3
Proof of Main Theorem in case deg(R)>6 5
Proof of Main Theorem in case deg(R)≤6 15
Reference 21

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