2020/04/19 by Rond, Guillaume
#Commutative Algebra (math.AC) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2004.08877
We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach algebra. In particular we construct an example of a commutative integral Banach algebra R such that the ring of formal power series over R is not flat over the ring of convergent power series over R.