For an easily comprehension of my questions I write some definitions:
An affine algebraic group scheme over $K$ is a representable group-functor from $K$-algebras category, with a finitely generated representing algebra.
An affine algebraic group over a $K$ is an affine algebraic variety with polynomials of definition having coefficients in $K$ equipped with a group structure compatible with the variety structure.
I know that every affine algebraic group over an infinite $K$ is equivalent to some affine algebraic group scheme over $K$.
I try to show if the converse is true but in my reference i can't read anithing helpful.
Can, some one, give me a hint to show that the converse is true or not?
I try to work with the rispective topologies but i'm confusing about topology over an affine algebraic group scheme. If i have $G : \mathcal{Alg}_K \longrightarrow \mathcal{Grp}$ representable with $A=K[X_1, \ldots , X_n]/I$, the isomorphism $G(K) \simeq Hom_K(A,K)$ allow me to equip G(K) with a topology? My intuition is that in some way i can use the Zarisky topology on $\mathbb{A}^n_K$ induced by the algebraic set defined by $I$. It is correct?