Do we have $ker (f)_{mathfrak p}simeq ker (g)$?

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Let $A,B$ be commutative rings with identity and $f:Ato B$ a homomorphism of rings. For any prime ideal $mathfrak q$ of $B$, denote $f^{-1}(mathfrak q)$ by $mathfrak p$, then $f$ induces the canonical homomorphism $g: A_{mathfrak p}to B_{mathfrak q}$, do we have $(ker f)_{mathfrak p}simeq ker g$?
abstract-algebra ring-theory commutative-algebra
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Let $A,B$ be commutative rings with identity and $f:Ato B$ a homomorphism of rings. For any prime ideal $mathfrak q$ of $B$, denote $f^{-1}(mathfrak q)$ by $mathfrak p$, then $f$ induces the canonical homomorphism $g: A_{mathfrak p}to B_{mathfrak q}$, do we have $(ker f)_{mathfrak p}simeq ker g$?
abstract-algebra ring-theory commutative-algebra
By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago
add a comment |
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Let $A,B$ be commutative rings with identity and $f:Ato B$ a homomorphism of rings. For any prime ideal $mathfrak q$ of $B$, denote $f^{-1}(mathfrak q)$ by $mathfrak p$, then $f$ induces the canonical homomorphism $g: A_{mathfrak p}to B_{mathfrak q}$, do we have $(ker f)_{mathfrak p}simeq ker g$?
abstract-algebra ring-theory commutative-algebra
Let $A,B$ be commutative rings with identity and $f:Ato B$ a homomorphism of rings. For any prime ideal $mathfrak q$ of $B$, denote $f^{-1}(mathfrak q)$ by $mathfrak p$, then $f$ induces the canonical homomorphism $g: A_{mathfrak p}to B_{mathfrak q}$, do we have $(ker f)_{mathfrak p}simeq ker g$?
abstract-algebra ring-theory commutative-algebra
abstract-algebra ring-theory commutative-algebra
asked 23 hours ago
Born to be proud
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By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago
add a comment |
By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago
By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago
add a comment |
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By Eric Wofsey's answer, it is not true. math.stackexchange.com/questions/2997819/…
– Born to be proud
22 hours ago
I wonder if jgon's answer is correct, can anybody help me check it? math.stackexchange.com/questions/2997043/…
– Born to be proud
22 hours ago