Green’s relation ℋ on the monoid of square matrices over a specific local ring

Abstract

Let [Formula: see text] be a commutative local ring whose maximal ideal is generated by a nilpotent element, and [Formula: see text] be the multiplicative monoid of the square matrices of order [Formula: see text] over [Formula: see text]. In this paper, we provide the construction of Green’s [Formula: see text]-equivalence classes in the multiplicative monoid [Formula: see text]. Then, we enumerate these classes in the special cases [Formula: see text] and [Formula: see text].