Year: 2017
Type: preprint
Abstract: A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to $\mathbb{R}$ and imposing the relation $i^2 = -1$. In this paper, we examine some of the elementary algebraic properties of such algebras, how they break-down when compared to standard grade-school algebra, and discuss how such properties are relevant to other areas of our research regarding algebras, such as the $\mathcal{A}$-calculus and the theory of $\mathcal{A}$-ODEs.
Source: arXiv (Cornell University)
Author: BeDell, Nathan
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2743884415