Abstract algebra MOC

Monoid

A monoid (𝑀, ⋅) is a Semigroup with an identity element. general In general elements needn’t have an inverse.

2. Associative 𝑎 ⋅(𝑏 ⋅𝑐) =(𝑎 ⋅𝑏) ⋅𝑐 for each 𝑎,𝑏,𝑐 ∈𝑀
3. Identity there exists (provably unique) 𝑒 ∈𝑀 such that 𝑎 ⋅𝑒 =𝑒 ⋅𝑎 =𝑎 for all 𝑎 ∈𝑀

A monoid may be generalized to a category, which can be thought of as a typed monoid. See also Monoid object.

---

develop | en | SemBr