Notation in Kronecker-Weber theorem Sorry for the dumb question but I don't understand a notation. I'm reading the notes of Culler about the Kronecker Weber theorem (see here) and at page 3 we have a finite extension of number field $L/K$ and we define $B=O_{L}$ the ring of integers. After that he define $$U^{(0)}=\hat{B}^{\times}.$$ **Question:** What $\times$ means in this situation? I got an internet research but I found nothing. I think is a standard notation but I just started to study this. Thank you.

The $\times$ simply means the unit group of the ring $\hat{B}$.