A coequality relation on a set with an apartness is defined by standard way as a consistent, symmetric and cotransitive relation. The coequality relation on the product $\prod X_i$ sets with apartnesses is called decomposible if it is determined by its special projections on $X_i$ respectively. This paper contains some theorems about characterization of decomposible coequality on the Cartesian product $\prod X_i$ of sets with apartnesses which are generalization of result of the main theorem in a paper by the author. As application of these theorems, we give the exact description of coideals of the commutative rings $\prod_{i=1}^{n}X_i$ and $\prod_{i=1}^{\infty}X_i$.