1. General information about bodies

1.1 Defining bodies and sub-bodies

Recall that any application (x, y) → x * y associating any pair (x, y) of E × E with an element of E, noted here x * y, is called an "internal composition law" (or more simply "operation") on a non-empty set E.

By way of example, here are some well-known laws of internal composition:

• in the set $\mathbb{Z}$ of integers, addition (p, q) → p + q and product (p, q) → pq are internal composition laws;

• in the set P(E) of parts of a given set E, the union (A, B) →