Corollary

Tag 06XN, permanent. Cite it as [Bourbaki, Tag 06XN].

Algebra, chapter VI, § 1. Ordered groups. Divisibility

— If an element $z$ of a lattice ordered group $G$ is coprime to each element $x_\alpha$ of a family having an infimum $y$ , then $z$ is coprime to $y$ .

This is an immediate consequence of the second formula (4).

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

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Cites

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