可逆性和中心对称

Pub Date : 2019-01-01 DOI:10.4134/JKMS.J180364

K. Choi, T. Kwak, Yang Lee

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引用次数: 6

摘要

．证明了约简环的一个与中心有关的性质，并在此基础上展开本文的论述。并证明了Wedderburn根与对称上中心环上所有幂零的集合重合，这意味着在对称上中心环上的多项式环上Jacobson半径、所有幂零的根和所有幂零的集合是相等的。证明了还原环是可逆过中心环，并且给定可逆过中心环，可以构造出各种可逆过中心环。研究了可逆过中心环和对称过中心环中自由基的结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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REVERSIBILITY AND SYMMETRY OVER CENTERS

. A property of reduced rings is proved in relation with centers, and our argument in this article is spread out based on this. It is also proved that the Wedderburn radical coincides with the set of all nilpotents in symmetric-over-center rings, implying that the Jacobson radi- cal, all nilradicals, and the set of all nilpotents are equal in polynomial rings over symmetric-over-center rings. It is shown that reduced rings are reversible-over-center, and that given reversible-over-center rings, various sorts of reversible-over-center rings can be constructed. The structure of radicals in reversible-over-center and symmetric-over-center rings is also investigated.

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