上三角矩陣環上具有交換跡的雙加性函數

Commuting Traces of Biadditive Maps On Upper Triangular Matrix Rings

郭覺照(Chiao-Chao Kuo)

指導教授 ： 劉承楷

國立彰化師範大學/理學院/數學系/碩士(2017年)

摘要

設R是一個環，n是一個大於1的整數，Tn(R)是以R為係數的nxn的上三角矩陣環。本篇論文主要的結果是刻畫Tn(R)n上具有交換跡之雙加性函數的結構定理。運用此定理，我們給出T(R)n上保持交換性加性函數的完整描述。

關鍵字

上三角矩陣環

並列摘要

Let R be a ring and let Tn(R) be the nxn upper triangular matrix ring over R , where n is an integer with n≥2 . We determine the form of a biadditive map B:Tn(R) x Tn(R) → Tn(R) which satisfies [B(x,x),x]=0 for all x belong to Tn(R).As an application, we characterize commutativity preserving additive maps on Tn(R).

並列關鍵字

Upper triangular matrix ring

參考文獻

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