🌀 abstract algebra

1. The problem is to explain the difference between a group and a groupoid. 2. A **group** is a set $G$ equipped with a binary operation $\cdot$ satisfying four properties:

1. Group theory studies algebraic structures called groups, which consist of a set $G$ and an operation $\cdot$ combining any two elements $a,b\in G$ to form another element $a\cdo

1. The term "module" in mathematics commonly refers to a generalization of vector spaces where scalars come from a ring instead of a field. 2. A module over a ring $R$ is an additi