example

algebraic_structures.md

@@ -0,0 +1,41 @@
+
+::: {.Definition #magma title="magma"}
+A magma is a set M with an operation ⋅ that sends any two elements a, b ∈ M to another element, a⋅b∈M. The symbol ⋅ is a general placeholder for a properly defined operation. This requirement that for all a, b in M, the result of the operation a⋅b also be in M, is known as the magma or closure property. 
+:::
+
+
+::: {.Definition #semigroup title="semigroup"}
+
+To understand semigroup, you need to know magma...
+
+:::: {#incmagma include="magma"}
+:::::
+
+... Now you know magma, let's see the definition of semigroup.
+
+(S, ⋅) is a semigroup if it is an associative magma.
+:::
+
+
+::: {.Definition #monoid title="monoid"}
+To understand monoid, you need to know semigroup...
+
+:::: {#incsemigroup include="semigroup"}
+:::::
+
+... Now you know semigroup, let's see the definition of monoid.
+
+A monoid is a semigroup with an identity element.
+:::
+
+
+::: {.Definition #group title="group"}
+To understand group, you need to know monoid...
+
+:::: {#incmonoid include="monoid"}
+:::::
+
+... Now you know monoid, let's see the definition of group.
+
+(S, ⋅) is a group is it is a monoid such that every element has an unique inverse.
+:::