AI 中文总结
本文研究Quandle代数，证明特征不为2的整环上有序交换Quandle的Quandle代数无非平凡幂等元，计算两类Quandle代数的自同构群，通过搜索得到换位子宽度为2的首批Quandle代数例子。
AI 中文摘要
本文发展了Quandle代数的理论。我们证明，在特征不为2的整环上，有序交换Quandle的Quandle代数无非平凡幂等元；还计算了任意交换环上平凡Quandle与奇数阶二面体Quandle的Quandle代数的自同构群，对偶数阶二面体Quandle给出部分结果；最后通过计算机搜索得到了换位子宽度为2的Quandle代数的首批例子。
英文摘要
The paper develops the theory of quandle algebras. We show that over integral domains of characteristic other than 2, quandle algebras of ordered commutative quandles have no nontrivial idempotents. We also compute the automorphism groups of quandle algebras of trivial quandles and dihedral quandles of odd orders over arbitrary commutative rings, with partial results for dihedral quandles of even orders. Finally, a computer search provides the first examples of quandle algebras of commutator width 2.
CommentsSeveral corrections made. 17 pages + references. Comments welcome
