definition of basic algebraic structures: magma, semigroup ,monoid, group.


Magma (or groupoid; not to be confused with groupoids in category theory) is a basic kind of algebraic structure. Specifically, a magma consists of a set equipped with a single binary operation that must be closed by definition.



Semigroup is an algebraic structure consisting of a set together with an associative binary operation.


Monoid is an algebraic structure with a single associative binary operation and an identity element.



Group is a set equipped with a binary operation that combines any two elements to form a third element in such a way that four conditions called group axioms are satisfied, namely closure, associativity, identity and invertibility.


algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A of finite arity (typically binary operations), and a finite set of identities, known as axioms, that these operations must satisfy.
...
https://www.youtube.com/watch?v=VGUOnmkaPvs