Abstract
Let [Formula: see text] be a commutative local ring whose maximal ideal is generated by a nilpotent element, and Mat[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 Mat[Formula: see text]. Then, we enumerate these classes in the special cases [Formula: see text] and [Formula: see text].
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