  Let $\mathbb{C}$ be field of complex numbers and $X$ be a connected quandle
of prime order. We study the regular representation of $X$ by describing the
quandle ring $\mathbb{C}[X]$ as direct sum of right simple ideals. We provide
description of tensor product of connected quandles of prime order. We further
discuss multiplicity freeness of quandle ring decomposition for connected
quandles of order $\leq 47$ and prove that $\mathbb{C}[X]$ decomposes
multiplicity free for affine connected quandle $X$.
