Morita contexts 環的性質

Abstract

在本篇論文中，我們延伸 Amitzur 對於 Morita contexts 的研究 [1]。並不假設 Morita contexts 有一致忠實的非奇異左理想，在本文章中我們給出了Morita contexts 是素環的充分必要，並且計算了中心。更進一步地，我們個別刻劃了滿足多項式恆等式與廣義多項式恆等式的Morita contexts，並且計算了多項式階數。我們在文中也給出了在經典Morita contexts 環上的應用。

In this thesis, we continue the study of Morita context in [1]. Without assumption that the Morita contexts has uniformly faithful, non-singular left ideal, here we give the necessary and sufficient condition of the prime Morita contexts, and compute its center.Furthermore, we characterize the Morita contexts to be a polynomial identity ring and generalized polynomial identity ring respectively, and compute its polynomial degree. We also give some applications on classical Morita context.