有效元素位于中心的环的结构

Pub Date : 2023-01-01 DOI:10.11650/tjm/231103

Tai Keun Kwak, Yang Lee, Yeonsook Seo

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引用次数: 0

摘要

利用Jacobson交换定理，研究了具有相同对角线和多项式环的矩阵环中有效元的结构。如果每个有效元素都在中心，则称环为正环。我们研究了PC环的结构与环的交换性的关系。证明了如果$R$是一个素数特征的PC环，则$R$上的多项式环也是一个PC环。每个周期PC环被证明是可交换的。

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Structure of Rings Whose Potent Elements are Central

We study the structure of potent elements in matrix rings with same diagonals and polynomial rings, motivated by Jacobson's theorem of commutativity. A ring shall be said to be PC if every potent element is central. We investigate the structure of PC rings in relation to the commutativity of rings. It is proved that if $R$ is a PC ring of prime characteristic then the polynomial ring over $R$ is also a PC ring. Every periodic PC ring is shown to be commutative.

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