Proposition 3

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

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

Let $E$ be an associative magma whose law is denoted by $\top$ . If an element $x$ of $E$ commutes with each of the elements $y$ and $z$ of $E$ , it commutes with $y \top z$ .

For

x \top (y \top z) = (x \top y) \top z = (y \top x) \top z \\ = y \top (x \top z) = y \top (z \top x) = (y \top z) \top x.

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

Cited by

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Cites

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