Correlation of regularity of two-dimensional and corresponding one-dimensional languages

We prove relations between regularity of two-dimensional and one-dimensional languages. Each two-dimensional language is corresponded to two sequences of one-dimensional languages corresponding to rows and columns of the two-dimensional language. For each of the following conditions the existence of both regular and nonregular two-dimensional languages is proved: all row and all column languages are regular; all row languages are regular, all column languages are nonregular; all column languages are regular, all row languages are nonregular; both all row and all column languages are nonregular.