hi can someone please help me to solve this problem:
Let A and B be two rings
we consider the functor F:ModA→ModB
Show that F is exact if and only if it transforms every exact sequence of A module into an exact sequence of B module.
all what i know is this:
we say that by definition F is an exact functor if it transforms any short exact sequence of A module into short exact sequence of B module.
but i didn't know how to show the equivalence.
thanks in advance
Let A and B be two rings
we consider the functor F:ModA→ModB
Show that F is exact if and only if it transforms every exact sequence of A module into an exact sequence of B module.
all what i know is this:
we say that by definition F is an exact functor if it transforms any short exact sequence of A module into short exact sequence of B module.
but i didn't know how to show the equivalence.
thanks in advance
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