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Showing 1 to 4 of 4 for “"Nonassociative algebra"”.
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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 …
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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 …
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Algebraic Structures and Variations: From Latin Squares to Lie Quasigroups
… 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 …
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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 …