MATRIX REPRESENTATION OF RECTANGULAR BANDS OF SEMIGROUPS
Xiaojiang Guo, K. P. Shum · Journal of Algebra and Its Applications · 2010
Abundant semigroups expressed as a perfect rectangular band of adequate semigroups will be investigated. A known theorem of Pastijn–Petrich in 1984 on perfect rectangular bands of inverse semigroups will be generalized from the class of regular semigroups to the class of abundant semigroups. A Rees matrix representation of such abundant semigroups will be established and some characterization theorems will be consequently given.