Quandle rings

Decomposition of quandle rings of dihedral quandles

Let $K = \mathbb R$ or $\mathbb C$ and $\mathcal R_n$ be the dihedral quandle of order $n$: In this article, we give decomposition of the quandle ring $K[\mathcal R_n]$ into indecomposable right $K[\mathcal R_n]$-modules for all even $n \in \mathbb N$. It follows that the decomposition of $K[\mathcal R_n]$ given in [EFT19, Prop. 4.18(2)] is valid only in the case when $n$ is not divisible by $4.$

Decomposition of quandle rings of Takasaki quandles

Let $K = \mathbb{R}$ or $\mathbb{C}$ and $T_{n}$ denote the Takasaki quandle of order $n$. In this article we provide decomposition of quandle ring $K[T_n]$ as direct sum of right simple ideals. This decomposition is equivalent to decomposition of regular representation \cite{EM18} of Takasaki quandles.

素数阶连通quandle的张量积与quandle环

Tensor product and quandle rings of connected quandles of prime order

该研究针对素数阶连通quandle，通过quandle环的右单理想直和刻画研究其正则表示，给出张量积刻画，讨论小阶连通quandle环的无重分解并证明仿射连通quandle的quandle环无重分解。

幂等元与理想在格架环中的幂

Idempotents and Powers of Ideals in Quandle Rings

本文研究了半拉丁格架环中的幂等元性质，并扩展了扩增理想幂的计算，应用于自同构群的计算。

关于拟群环中幂等元的一个注记

A note on idempotents in quandle rings

本文证明有限拉丁拟群整数环的幂等元平凡性猜想对拉丁二面体拟群成立，并给出反例。

中顶quandle环的零因子与增广猜想

The zero divisor and augmentation conjectures for medial quandle rings

本文验证了中顶quandle的零因子与增广猜想，刻画了相关类quandle及有限Alexander quandle对应陈述成立的整环，推进了quandle环相关猜想的研究。