Green's relation Script capital H on the monoid of square matrices over a specific local ring

Let R be a commutative local ring whose maximal ideal is generated by a nilpotent element, and Mat(n,R) be the multiplicative monoid of the square matrices of order n over R. In this paper, we provide the construction of Green's Script capital H-equivalence classes in the multiplicative monoid Mat(n,R). Then, we enumerate these classes in the special cases R = Z/p(d)Z and R = F-q[x]/< x(d)>.