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Mariano Suárez-Álvarez
Mariano Suárez-Álvarez
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k is a fieldLet $k$ be a field,L $L$, H is$H$ extension fields of k $k$, and $G=L\otimes_k H$,. I wonder why  (I want to know the proof but I can't find) the prime ideal of G$G$ must be maximal  ,and and its properties:

a) if L$L$ is spearableseparable over k$k$, then G$G$ is reduced.

b) if L$L$ is algebraic and purely inseparable over k $k$,then G then $G$ has a unique prime ideal.

k is a field ,L , H is extension fields of k , $G=L\otimes_k H$, I wonder why(I want to know the proof but I can't find) the prime ideal of G must be maximal  ,and its properties:

a) if L is spearable over k, then G is reduced

b) if L is algebraic and purely inseparable over k ,then G has a unique prime ideal

Let $k$ be a field, $L$, $H$ extension fields of $k$, and $G=L\otimes_k H$. I wonder why  (I want to know the proof but I can't find) the prime ideal of $G$ must be maximal, and its properties:

a) if $L$ is separable over $k$, then $G$ is reduced.

b) if $L$ is algebraic and purely inseparable over $k$, then $G$ has a unique prime ideal.

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TOM
TOM
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question about tensor of two fields

k is a field ,L , H is extension fields of k , $G=L\otimes_k H$, I wonder why(I want to know the proof but I can't find) the prime ideal of G must be maximal ,and its properties:

a) if L is spearable over k, then G is reduced

b) if L is algebraic and purely inseparable over k ,then G has a unique prime ideal