# 臺灣博碩士論文加值系統

(44.192.79.149) 您好！臺灣時間：2023/06/03 00:43

:::

### 詳目顯示

:

• 被引用:0
• 點閱:55
• 評分:
• 下載:0
• 書目收藏:0
 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 IAbstract II致謝 IIIContents IVIntroduction and Results 1Preliminaries 3Proof of Main Theorem in case deg(R)>6 5Proof of Main Theorem in case deg(R)≤6 15Reference 21
 [1] K.I. Beidar, On functional identities and commuting additive mappings, Comm. Algebra 26 (1998), 1819--1850.[2] K.I. Beidar, W.S. Martindale 3rd and A.V. Mikhalev, "Rings with Generalized Identities", Marcel Dekker, Inc., New York--Basel--Hong Kong, 1996.[3] K.I. Beidar, M. Bresar, M. A. Chebotar and W. S. Martindale 3rd, On Herstein's Lie map conjectures II, J. Algebra 238 (2001), 239--264.[4] M. Bresar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003--1006.[5] M. Bresar, Jordan derivations revisited, Math. Proc. Camb. Phil. Soc. 139 (2005), 411--425.[6] M. Bresar, On generalized biderivations and related maps, J. Algebra 172 (1995), 764--786.[7] M. Bresar, M.A. Chebotar and W.S. Martindale 3rd, "Functional Identities", Birkhaus-er, 2007.[8] M. Bresar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321--322.[9] M. Fosner and D. Ilisevica, On a class of projections on *-rings, Comm. Algebra 33 (2005), 3293--3310.[10] M. Fosner and J. Vukman, On some equations in prime rings, Monatsh. Math. 152 (2005), 135--150.[11] I.N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104--1110.[12] N. Jacobson, Lie and Jordan Triple Systems, Amer. J. Math. 71 (1949), 149--170.[13] W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228} (1977), 39--64.[14] W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), 503--529.[15] T.-K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20 (1992), 27--38.[16] T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999), 4057--4073.[17] C.-K. Liu, The structure of triple derivations on semisimple Banach *-algebras, Quart. J. Math. 68 (2017), 759--779.[18] C.-K. Liu, An Engel condition with two generalized derivations in prime rings, Comm. Algebra 49 (2021), 836-849.[19] K.-S. Liu, A theorem on derivations on prime rings, J. Aust. Math. Soc. 91 (2011), 219--229.[20] L.L. Stacho and B. Zalar, Bicircular projections on some matrix and operator spaces, Linear Algebra Appl. 384 (2004), 9--20.[21] J. Vukman, I. Kosi-Ulbl and D. Eremita, On certain equations in rings, Bull. Austral. Math. Soc. 71 (2005), 53--60.
 電子全文(網際網路公開日期：20270717)
 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄

 1 對合環上的導算 2 質環的李理想上的n階加性交換性函數 3 質環上的李導算 4 質環上冪交換性函數的推廣 5 質環上的喬登τ-導算 6 質環上的導算合成 7 質環與導算子式 8 質環上單邊理想的導算 9 質環上之單邊理想的導算等式 10 非結合質環之導算 11 斜對稱元冪次具中心值之導算 12 對合環與導算 13 特徵工的質環上之導算

 無相關期刊

 1 數學創意教學活動對國民中學數理資優學生擬題學習成效之研究 2 探討以接受與承諾治療方案介入自閉症類群家長之成效 3 引擎機油黏度對空污之影響 4 魅力領導與主管知覺部屬效忠之關係：探討不道德利組織行為之中介效果與道德認定之干擾效果 5 關於由乘積交換規範場論產生的方程的解的分類 6 海外投資對企業社會責任之影響: 以外資持股、外國董事為調節變項 7 汽車冷凝器散熱改善之研究 8 建構蝴蝶蘭之CymMV病毒誘導增強遺傳表現系統 9 探討含氮接受子對陰離子之作用暨螢光淬滅 10 碎形結合資訊科技融入高中數學線性變換課程之研究 11 重大裁罰案件對上市金融業股價報酬及財務績效之影響 12 台灣遊覽車營運狀況差異性分析 13 保險業務員具有長照制度認知與長照險知識 對於長照險銷售意願之影響 14 新冠肺炎疫情期間職家衝突、居家辦公、工作滿意與工作績效之關聯性研究—以某縣市政府為例 15 銀行的董監事責任險是否促進銀行收入與資產多角化

 簡易查詢 | 進階查詢 | 熱門排行 | 我的研究室