Definition 2

Tag 055D, permanent. Cite it as [Bourbaki, Tag 055D].

Algebra, chapter I, § 1. Laws of composition; associativity; commutativity

Let E be a magma and $\tau$ denote its law of composition. The law of composition $(x, y) \mapsto y \tau x$ on E is called the opposite of the above. The set E with this law is called the opposite magma of E.

Let E and E' be two magmas; we shall denote their laws by the same symbol $\tau$ . Conforming with the general definitions (Set Theory, IV, § 1, no. 5), a bijective mapping f of E onto E' such that

f(x \tau y) = f(x) \tau f(y)

for every ordered pair

(x, y) \in E \times E

is called an isomorphism of E onto E'. E and E' are said to be isomorphic if there exists an isomorphism of E onto E'.

More generally:

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

*Set Theory*, IV, § 1, no. 5