Greenʹs relations in the matrix semigroup Mn(S) Original Research Article

We investigate Greenʹs relations in the multiplicative semigroup of matrices Mn(S), where S is any strong ideal subset of R+. First we characterize the structures of R, L, D, and H classes in Mn(S). Our results generalize the corresponding known results in the semigroup Mn(R+). Then we prove that J = D in Mn(S*), where S* is any strong ideal subset of R+ which has no elements less than 1 except 0.