A Ring Epimorphism that is not a Surjection

A Ring Epimorphism that is not a Surjection

Consider the inclusion  i : \mathbb{Z} \to \mathbb{Q} . It is clearly not surjective. However, given any two ring homomorphismsf ,g  : \mathbb{Q} \to R such thatf \circ i = g \circ i, it holds that f=g because ring homomorphisms out of the rationals that agree on the integers must agree everywhere. So,  i is an epimorphism in Ring.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s