3 citations · 3 across the 3 of their papers we have counts for
8 papers
A further study of quandles and quandle rings
Gregory Churchill, Indu Rasika Churchill, Neranga Fernando +1
We investigate core quandles and idempotents in quandle rings of core quandles. We answer several questions on the rank of core quandles and nontrivial idempotents in quandle rings…
Singquandles, Psyquandles and Singular Knots: A Survey
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi +1
In this short survey we review recent results dealing with algebraic structures (quandles, psyquandles, and singquandles) related to singular knot theory. We first explore the sing…
Singquandle Shadows and Singular knot Invariants
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi
We introduce shadow structures for singular knot theory. Precisely, we define \emph{two} invariants of singular knots and links. First, we introduce a notion of action of a singqua…
Cocycle Invariants and Oriented Singular Knots
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi +1
We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both r…
Polynomial Invariants of Singular Knots and links
Jose Ceniceros, Indu R. Churchill, Mohamed Elhamdadi
We generalize the notion of the quandle polynomial to the case of singquandles. We show that the singquandle polynomial is an invariant of finite singquandles. We also construct a…
The Cocycle structure of the Alexander -quandles on finite fields
Indu Rasika Churchill, Mohamed Elhamdadi, Neranga Fernando
We determine the second, third, and fourth cohomology groups of Alexander -quandles of the form , where denotes the finite field of…
Singular Knots and Involutive Quandles
Indu R. U. Churchill, M. Elhamdadi, M. Hajij +1
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings…
-Racks, -Quandles, their Extensions and Cohomology
Indu R. U. Churchill, M. Elhamdadi, M. Green +1
The purpose of this paper is to introduce and study the notions of -rack and -quandle which are obtained by twisting the usual equational identities by a map. We provide some…