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Section A.2 Algebraic Structures
Subsection Grouplike Structures
Definition A.5.
Let \(*\) be a binary operation on a set \(S\text{.}\) We define the following:
The pair \((S,*)\) is called a magma.
A semigroup is an associative magma.
A monoid is a semigroup with an identity element.
A group is a monoid with inverses.
An abelian group is a commutative group.
Definition A.6.
Let \(*\) be a partial binary operation on a set \(S\text{.}\) We define the following:
The pair \((S,*)\) is called a partial magma.
A semigroupoid is an associative partial magma.
A small category is a semigroupoid with an identity element.
A groupoid is a small category with inverses.
Subsection Ringlike Structures
Definition A.7.
Subsection Latticelike Structures
Definition A.8.
