Commutativity conditions for rings: 1950–2005
Commutativity conditions for rings: 1950–2005
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DOI：
10.1016/j.exmath.2006.07.001
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发表时间：
2007-05
影响因子：
0.7
通讯作者：
James Pinter-Lucke
中科院分区：
文献类型：
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作者：
James Pinter-Lucke
在过去的55年里，已经有许多关于强制环是可交换的条件的结果。这些结果是由雅各布森的著名结果刺激的，并由赫斯坦广泛发展。本文将根据结果是否来自Herstein条件的变化，依赖于一般多项式条件，依赖于导数的存在，或者环是否具有使交换性更容易获得的特殊性质来组织结果来考察该区域。最后，最新的条件与产品集有关，并导致了一个新的查询领域的结果。
During the last 55 years there have been many results concerning conditions that force a ring to be commutative. These results were stimulated by Jacobson's famous result and were extensively developed by Herstein. This paper will survey the area by organizing the results according to whether they come from variations on Herstein's conditions, depend on general polynomial conditions, depend on the presence of a derivation, or whether a ring has special properties that make commutativity more easily accessible. Finally, the most recent conditions concern product sets and lead to results in a new area of inquiry.