The matrix envelope of a semigroup (Q1118044)

The purpose of this paper is to faithfully represent a semigroup S which satisfies DCC on both left and right ideals by row-monomial matrices over a group with zero. If there are only finitely many left ideals and right ideals then the matrices are finite. \{Reviewer's remark: the representation is a direct sum of three distinct representations. Whilst two of these are indeed by row-monomial matrices, the third is in fact by column-monomial matrices. Transposing the matrices unfortunately leads to an anti-representation in that case.\}