n-dimensional observables on k-perfect MV-algebras and k-perfect effect algebras. I. Characteristic points

In the paper, we investigate a one-to-one correspondence between n-dimensional observables and spectral resolutions with values in kind of lexicographic form quantum structures like perfect MV-algebras or effect algebras. The multidimensional version this problem is more complicated than one-dimensional one because if our algebraic structure k-perfect for k>1, then even two-dimensional case have characteristic points. obtained results are also applied to existence an meet joint observable n on MV-algebra. divided into two parts. Part I, present notions accent type algebras MV-algebras. We concentrate points main body II where relations presented.