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Aug 6, 2015 at 14:03 comment added abx I think you are confused about the meaning of "integral". It means that any element of $B$ is annihilated by a monic polynomial with coefficients in $A$. $\mathbb{R}$ is certainly not integral over $\mathbb{Z}$.
Aug 6, 2015 at 13:22 vote accept user237522
Aug 6, 2015 at 13:22
Aug 6, 2015 at 13:11 history answered Dominic van der Zypen CC BY-SA 3.0