Let $(X,\ast)$ be an algebraic structure. The binary operation "$\ast$" is called associative if $(x\ast y)\ast z=x\ast (y\ast z)$ holds for any three elements \(x,y,z\in X\).
Note: The parentheses in the above definition are a notation of the composition of the function $"\ast$" with itself and it is required that both sides of the following equation are equal:
$$\ast(\ast(x,y),z)=\ast(x,\ast(y,z)).$$
Corollaries: 1
Axioms: 1 2 3
Chapters: 4 5 6 7
Corollaries: 8
Definitions: 9 10 11 12 13
Examples: 14 15
Lemmas: 16
Proofs: 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Propositions: 31 32 33 34 35 36 37
Solutions: 38