When we dealt with number systems, we became familiar for instance with the natural numbers together with addition $(\mathbb N, + )$, the integers together with addition and multiplication $(\mathbb Z, +, \cdot),$ or the real numbers together with addition and multiplication $(\mathbb R , + ,\cdot).$
In general, if on a set one or more operation, like addition or multiplication, is defined, usually these operations "shape" a structure inside the set, called an algebraic structure.
In this part, we start our treatise of algebra with a quick overview of the different algebraic structures. In later parts, we will dive deeper into the theory of the separate algebraic structures.
Motivations: 1 Explanations: 1
Definitions: 3 4
Motivations: 5 6