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Abstract algebra - Coggle Diagram
Abstract algebra
Group
Definition
A semigroup (G, ◦) is called a group if
(1) there exists in G an element e, called a right identity, such that x ◦ e = x for all x in G.
(2) for each element x of G there corresponds an element y of G, called a right inverse of x, such that x ◦ y = e.
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Binary operations
Associative operations
Definition
The operation ◦ is said to be associative if (x ◦ y) ◦ z = x ◦ (y ◦ z) is valid for all x, y, z ∈ S
Semigroup
the pair (S, ◦) is called a semigroup
Commutative operations
Definition
The operation ◦ is said to be commutative if x◦y=y◦x is always valid for all x, y ∈ S