  In this article, we classify connected commutative (locally) Nash groups,
which is a continuation of our previous work on the classification of abelian
Nash manifolds. Our results generalize the classification of the
one-dimensional case by Madden-Stanton and the two-dimensional case by
Baro-Vicente-Otero. Moreover, we determine the affineness and toroidal
affinenese of a connected commutative Nash group.

Algebraic Geometry