[[R-algebra]]
# Associative algebra over a commutative ring

Let $R$ be a [[commutative ring]].
An **$R$-semigroup** $T$ can be viewed in two equivalent ways: #m/def/ring 
1. As an $R$-[[R-algebra|algebra]] which is associative;
2. As a [[rng]] $T$ equipped with an $R$-action.

It is thus a [[Semigroup object]] in [[Category of modules over a commutative ring|$\lMod R$]]

#
---
#state/tidy | #lang/en | #SemBr