# ac.commutative algebra – Gelfand ring in Bourbaki’s exercises

In Bourbaki’s General Topology, Chapitre III §6 Exercise 11, they define a Gelfand Ring as a
topological ring $$A$$ such that

1. The set $$A^*$$ ($$=A^{-1}$$) of invertibles is open.
2. The uniform structure induced on $$A^*$$ by the given one on $$A$$ is compatible with the group structure.

Of course, the product being continuous, this amounts to only ask that $$xmapsto x^{-1}$$ be continuous.
My question is (as commutativity is not required):

Is there a link between this notion and the one commonly accepted in commutative algebra? (see https://en.wikipedia.org/wiki/Gelfand_ring)