Sebastian Alevad: Algebraiska strukturer – Halvgrupper, Grupper, Ringar, Kroppar

Abstract

This essay will function as an introduction to algebraic structures. In abstract algebra - or as it is also called, modern algebra - one studies the algebraic structures, these structures are defined as a set of elements equipped with a number of operations. In this essay I will only handle structures equipped with one or two operations, these are for example: addition, multiplication, geometric rotations, matrix addition and matrix multiplication. Depending on the algebraic structure, it must abide by a certain set of basic properties. These basic properties are the commutative and associative law for addition and multiplication and the distributive law for multiplication over addition. The set of elements does not have to be finite, if a neutral element and an inverse element exists or not. Even though there are more structures, this essay will contain following algebraic structures: semigroups, groups, rings and fields. But each of these four individual structures can be broken down into different categories, depending on if they abide by one or more of our basic properties. 

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