We classify the pairs (A,D) consisting of an
(ϵ,Γ)-olor-commutative associative algebra A with an identity
element over an algebraically closed field F of characteristic zero and a
finite dimensional subspace D of (ϵ,Γ)-color-commutative
locally finite color-derivations of A such that A is Γ-graded
D-simple and the eigenspaces for elements of D are Γ-graded. Such
pairs are the important ingredients in constructing some simple Lie color
algebras which are in general not finitely-graded. As some applications, using
such pairs, we construct new explicit simple Lie color algebras of generalized
Witt type, Weyl type.Comment: 15 page