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
asked 23 hours ago
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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
asked 23 hours ago
Born to be proud
735510
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 |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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
asked 23 hours ago
Born to be proud
735510
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
735510
asked 23 hours ago
Born to be proud
735510
asked 23 hours ago
Born to be proud
735510
asked 23 hours ago
Born to be proud
735510
asked 23 hours ago
Born to be proud
735510
735510
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