What text or any document that has gathered this part of Algebra theory. Thanks. Pd: I seek on variety’s book of commutative algebra but the subject is partially dealt

I am trying to solve the following problem: For each rational prime $p$, describe the decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields, where $\mathbb{Q}_p$ is the field of $p$-adic numbers. I know that the tensor product of $2$ extensions of a field one of which is finite is Artinian […]

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