论文标题
基金会，免费产品和拼图覆盖物
Idempotents, free products and quandle coverings
论文作者
论文摘要
在本文中，我们调查了Quandle环中的同一源，并将其与Quandle覆盖物联系起来。我们证明，有限类型的难题的整体环形环，它们是尼斯基础搜索的非平凡覆盖物，可以无限地承认许多非平凡的依恋者，并给出他们的完整描述。我们表明，所有这些愿望的集合本身就形成了一个困境。作为一种应用，我们推断出非平凡的长结的打结环的环形环允许非平凡的愿望。我们考虑了Quandles的免费产品，并证明了自由难题的整体难题仅具有琐碎的态度，从而为无限的Quandles带来了这种属性。我们还对工会的难题和某些扭曲工会的难题中的同胞描述。
In this paper, we investigate idempotents in quandle rings and relate them with quandle coverings. We prove that integral quandle rings of quandles of finite type that are non-trivial coverings over nice base quandles admit infinitely many non-trivial idempotents, and give their complete description. We show that the set of all these idempotents forms a quandle in itself. As an application, we deduce that the quandle ring of the knot quandle of a non-trivial long knot admit non-trivial idempotents. We consider free products of quandles and prove that integral quandle rings of free quandles have only trivial idempotents, giving an infinite family of quandles with this property. We also give a description of idempotents in quandle rings of unions and certain twisted unions of quandles.
