An integral morphism is a morphism 
of schemes such that, for
every affine scheme 
open in 
, its inverse image 
is an affine scheme 
and every element
of 
satisfies a monic polynomial with coefficients
in the image of the induced ring
homomorphism 
(Stacks Project n.d., Tag 01WG). Thus the induced ring
homomorphism is integral, although it need not be injective.
It is enough to check this condition on an affine open
cover of 
.
For example, for a field 
, the morphism ![Spec(k[epsilon]/(epsilon^2))->Spec(k)](/images/equations/IntegralMorphism/Inline10.svg)
is integral. Each element 
of the ring of dual
numbers satisfies the monic polynomial 
with coefficients
in 
.
