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Full-Text Articles in Algebra
Varieties Of Nonassociative Rings Of Bol-Moufang Type, Ronald E. White
Varieties Of Nonassociative Rings Of Bol-Moufang Type, Ronald E. White
All NMU Master's Theses
In this paper we investigate Bol-Moufang identities in a more general and very natural setting, \textit{nonassociative rings}.
We first introduce and define common algebras. We then explore the varieties of nonassociative rings of Bol-Moufang type. We explore two separate cases, the first where we consider binary rings, rings in which we make no assumption of it's structure. The second case we explore are rings in which, $2x=0$ implies $x=0$.
Quandles That Are Knot Quandles, Jason Haskell
Quandles That Are Knot Quandles, Jason Haskell
All NMU Master's Theses
There are many papers that introduce the relationship between knots and quandles which are written tersely and focus mainly on applications or implications. Here, we will take time to explain in depth how to derive quandles from oriented knots. Starting with an rigorous introduction to what a knot is and what a quandle is, we will also define the Fundamental Quandle of a knot and the relationship between colorings of a knot and the homomorphisms from an arbitrary quandle to a Fundamental Quandle. Then using this foundation, we will examine two sets of knots that produce quandles that contain subquandles …
Kissing The Archimedeans, Anthony Webb
Kissing The Archimedeans, Anthony Webb
All NMU Master's Theses
In this paper the three dimensional kissing problem will be related to the Platonic and Archimedean solids. On each polyhedra presented their vertices will have spheres expanding such that the center of each of these outer spheres are the vertices of the polyhedron, and these outer spheres will continue to expand until they become tangent to each other. The ratio will be found between the radius of each outer sphere, and the radius of an inner sphere such that each inner sphere's center is the circumcenter of the polyhedron, and the inner sphere is tangent to each outer sphere. Every …