Proposition 4
Tag 056Z, permanent. Cite it as [Bourbaki, Tag 056Z].
Algebra, chapter I, § 2. Identity element; cancellable elements; invertible elements
Let E be a monoid and x and y invertible elements of E with inverses x' and y' respectively. Then y' x' is the inverse of x y.
This follows from the relation
and the analogous calculations for (x y) (y' x').
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
- § 2. Identity element; cancellable elements; invertible elements
- Lemma 2, § 2
- Remark, § 2
- Corollary 1, § 2
- Proposition 6, § 2
- Theorem 1, § 2
- Example, § 4
Cites
Nothing.