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May 10, 2023 at 0:02 comment added Syu Gau @AchimKrause Great Couterexample! Thanks!
May 9, 2023 at 8:26 comment added Achim Krause I don't think so. For example for $A=B=\mathbb{F}_2[C_2]$, the respective Picard groups are trivial, but for $A\otimes B$ the Picard group is given by $\mathbb{Z}$.
May 9, 2023 at 4:50 history asked Syu Gau CC BY-SA 4.0