Green H-relation of the square matrices over a local ring whose maximal
ideal is generated by a nilpotent element
Abstract
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 article, we provide (1) the construction of the Green’s
$H$-equivalence classes in $\Mat (n, R)$, and (2) the
enumeration of the Green’s $H$-equivalence classes in
$\Mat (n, Z/ p^d Z)$.
