Abstract
Algebra is the branch of mathematics that uses letters in the place of numbers, where the letters stand for variables or constants that are used in mathematical expressions. It is the study of such mathematical symbols and the rules for manipulating them, and it is a powerful tool for problem solving in science and engineering. Algebra covers many areas such as elementary algebra, linear algebra, and abstract algebra. Elementary algebra includes the study of simultaneous equations; quadratic equations; polynomials; indices and logarithms. Linear algebra is concerned with the solution of a set of linear equations and the study of matrices. Abstract algebra is concerned with the study of abstract algebraic structures such as groups, rings, fields, and vector spaces.
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Notes
- 1.
Recall that \({\mathbb{Z}}/n{\mathbb{Z}} = {\mathbb{Z}}_n = \left\{ {[a]_n :0 \le a \le n - 1} \right\} = \left\{ {[0]_n ,[1]_n , \ldots ,[n - 1]_n } \right\}\).
- 2.
A finite division ring is actually a field (i.e., it is commutative under multiplication), and this classic result was proved by Wedderburn.
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O’Regan, G. (2023). Algebra. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_5
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DOI: https://doi.org/10.1007/978-3-031-26212-8_5
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