Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 11 of 11 for “"Nonassociative"”.
-
Subexponentials in Nonassociative Lambek Calculus
We focus on a family on noncommutative nonassociative substructural logics enriched with subexponentials, unary modalities licensing local application of structural rules. Primarily, we prove upper and lower bounds on complexity of provability in a broad class of these logics. To uniformly frame …
-
On Nonassociative Division Rings and Projective Planes
… and commutative properties. The resulting nonassociative division ring is referred to as a ``semifield" in this paper. Semifields have intimate ties to finite projective planes. In short, a finite projective plane with certain restrictions gives rise to a semifield, and, in turn, a finite …
-
Varieties of Nonassociative Rings of Bol-Moufang Type
… a more general and very natural setting, \textit{nonassociative rings}.</p> <p>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 …
-
Graded-commutative nonassociative algebras: higher octonions and Krichever-Novikov superalgebras; their structures, combinatorics and non-trivial cocycles.
… of real (resp. complex) noncommutative and nonassociative algebras $\bbO_{p,q}$ (resp. $\bbO_{n}$) generalizing the algebra of octonion numbers $\bbO$. This generalization is similar to the one of the algebra of quaternion numbers in Clifford algebras. Introduced by Morier-Genoud and …
-
QUOTIENTS, EQUIVALENCE RELATIONS, AND NORMALITY IN NON-ASSOCIATIVE ALGEBRA WITH REGARDS TO LOOPS AND QUASIGROUPS
… quasigroups, and related theorems and varieties. Nonassociative algebra is a relatively new area of mathematics, it came about in the past hundred years, and has started making progress in the past 60 years. In nonassociative algebra, varieties do not necessarily satisfy associativity. Several …
-
The behavior of laterally loaded single piles and group piles in sand
… isotropic hardening constitutive model with nonassociative flow rule is used to model the behavior of sand. The purpose of the study is to gain a better understanding of the soil and pile behavior of laterally loaded single and group piles using the finite element approach.
-
Zorn vector matrices over commutative rings and the loops arising from their construction
… which Paige used to construct simple nonassociative Moufang loops over finite fields can, in fact, be done over any commutative ring with the proper adjustments. The resulting loops are still Moufang, but no longer simple in general. Given a commutative ring and an ideal of that ring, …
-
On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
… Although quaternionic automorphic loops are nonassociative, many of their properties are reminiscent of the generalized quaternion groups.</p> <p>Lastly, we find varieties of quasigroups which are isotopic to commutative Moufang loops and prove their full characterization. Moreover, we define …
-
Cayley-Dickson Loops
… Cayley-Dickson algebras and loops become nonassociative, which presents a significant challenge in their study.</p> <p>We begin by describing basic properties of the Cayley–Dickson loops <em>Q<sub>n</sub></em>. We establish or recall elementary facts about <em>Q<sub>n</sub></em>, e.g., …
-
Algebraic Structures and Variations: From Latin Squares to Lie Quasigroups
<p>In this Master's Thesis we give an overview of the algebraic structure of sets with a single binary operation. Specifically, we are interested in quasigroups and loops and their historical connection with Latin squares; considering them in both finite and continuous variations. We also consider …
-
Relaciones entre la estructura de un álgebra de Lie y el retículo de sus ideales
The lattice of ideals of a Lie algebra is closely related with the structure of the algebra. In the first chapter, some classes of Lie algebras are selected. It is studied if their lattices of ideals can determinate their algebraic structures. In the second chapter, two classes of lattices are …