First of all, we want to define formally, what exactly shall be understood under an algebraic structure. We start with the concept of a binary operation.

Definition: Binary Operation 

A binary operation \(\ast\) on a set \(X\) ist a total function $\ast :X\times X\to X$ mapping all pairs $x,y\in X\times X$ to a specific $z\in X,$ formally $$x\ast y:=\ast (x,y)=z.$$

| | | | | created: 2016-09-04 19:02:19 | modified: 2019-08-04 06:56:56 | by: bookofproofs | references: [6907]