Let R be a ring, and I be an ideal of G.
Show that there is a one to one and onto correspondence between the subrings of R/I and those subrings of R which contain I.
Hint: maybe the "natural" homomorphism f: R-> R/I defined by f(x)= x+I
can someone help me please
Saying "one-to-one and onto correspondence" is not necessary because a one-to-one correspondence is defined as a one-to-one and onto.Originally Posted by evonnova
Let R be a ring, and I be an ideal of G.
Show that there is a one to one and onto correspondence between the subrings of R/I and those subrings of R which contain I.
Hint: maybe the "natural" homomorphism f: R-> R/I defined by f(x)= x+I
can someone help me please
Defineto be the natural projection. If
is a subring of
then
is a subring of
. If
is a subring of
is a subring of
Letbe the set of all subrings of
and
be the set of all subrings of
as
for all
.
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