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