Quandle rings
Valeriy G. Bardakov, Inder Bir Singh Passi, Mahender Singh
TL;DR
This paper introduces the concept of quandle rings, establishing a new algebraic framework that parallels group rings, and explores the relationship between quandles and their associated rings.
Contribution
It proposes the first comprehensive theory of quandle rings and investigates their connections to quandle structures.
Findings
Established foundational properties of quandle rings
Explored algebraic relationships between quandles and quandle rings
Provided insights into the structure of quandle rings
Abstract
In this paper, a theory of quandle rings is proposed for quandles analogous to the classical theory of group rings for groups, and interconnections between quandles and associated quandle rings are explored.
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