论文标题
Zero divisors and Idempotents in Quandle环
Zero-divisors and idempotents in quandle rings
论文作者
论文摘要
该论文进一步发展了Quandle环的理论，这是作者在最近的一项工作中引入的。定义了难题的有序性，并给出了许多有趣的订购难题示例。事实证明，半拉丁蛋白的左或右订购搜索的环形环没有零分量。计算并使用某些有趣的搜索群的Quandle环中的dempotents来确定这些环中最大搜索的集合。对基于企业的理解进一步应用，以确定这些难题环的自身形态群体。同样，在少数情况下引入并计算了Quandle环的换向器宽度。本文通过评论Quandle环与其他众所周知的非缔合代数的关系。
The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of orderable quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have no zero-divisors. Idempotents in quandle rings of certain interesting quandles are computed and used to determine sets of maximal quandles in these rings. Understanding of idempotents is further applied to determine automorphism groups of these quandle rings. Also, commutator width of quandle rings is introduced and computed in a few cases. The paper conclude by commenting on relation of quandle rings with other well-known non-associative algebras.
