We associate to every quandle X and an associative ring with unity k, a nonassociative ring
k [X] following [3]. The basic properties of such rings are investigated. In particular, under the …

In this paper, we introduce the new construction of quandles. For a group G and a subset A
of G we construct a quandle Q (G, A) which is called the (G, A)-quandle and study properties …

The paper develops the theory of quandle rings introduced by the authors in a recent work.
Orderability of quandles is investigated and many interesting examples of such quandles …

We show that quandle rings and their idempotents lead to proper enhancements of the well-
known quandle coloring invariant of links in the 3-space. We give explicit examples to show …

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 nontrivial …

We generalise the construction of $ Q $-family of quandles and $ G $-family of quandles
which were introduced in the paper of A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro, and find …

In this paper we study some algebraic properties of the rack structure as well as the
representation theory of it, following the ideas given by M. Elhamdadi and EM Moutuou …

Abstract Let K= R or C and R n be the dihedral quandle of order n. In this article, we give
decomposition of the quandle ring K [R n] into indecomposable right K [R n]-modules for all …

Quandle representations are homomorphisms from a quandle to the group of invertible
matrices on some vector space taken with the conjugation operation. We study certain …

This paper is a first step in constructing the category of braided sets and its closest relative,
the category of Yang–Baxter sets. Our main emphasis is on the construction of morphisms …