how to show that $E(A,B_1oplus B_2)cong E(A,B_1)times E(A,B_2)$
$begingroup$
Show that $E(A,B_1oplus B_2)cong E(A,B_1)times E(A,B_2)$.$E(A,B)$ here means the set of equivalence classes of extensions of A by B.It's a exercise from GTM 4 ,Chapter 3,but I don't know how to prove it.
commutative-algebra
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
$endgroup$
add a comment |
$begingroup$
Show that $E(A,B_1oplus B_2)cong E(A,B_1)times E(A,B_2)$.$E(A,B)$ here means the set of equivalence classes of extensions of A by B.It's a exercise from GTM 4 ,Chapter 3,but I don't know how to prove it.
commutative-algebra
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
$endgroup$
$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50
add a comment |
$begingroup$
Show that $E(A,B_1oplus B_2)cong E(A,B_1)times E(A,B_2)$.$E(A,B)$ here means the set of equivalence classes of extensions of A by B.It's a exercise from GTM 4 ,Chapter 3,but I don't know how to prove it.
commutative-algebra
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
$endgroup$
Show that $E(A,B_1oplus B_2)cong E(A,B_1)times E(A,B_2)$.$E(A,B)$ here means the set of equivalence classes of extensions of A by B.It's a exercise from GTM 4 ,Chapter 3,but I don't know how to prove it.
commutative-algebra
commutative-algebra
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
asked Dec 24 '18 at 14:44
Daniel XuDaniel Xu
877
877
$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50
add a comment |
$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50
$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50
add a comment |
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$begingroup$
What are $A,B_1,B_2$?
$endgroup$
– Rafay Ashary
Dec 24 '18 at 14:48
$begingroup$
modules over a ring
$endgroup$
– Daniel Xu
Dec 24 '18 at 14:50