2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152399Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rectangular band analogs and the ``wreath'' version of them are studied in detail. We introduce the ``fine'' equivalence relations leading to ``multidimesional'' eggbox diagrams. They are full images of Green's relations on corresponding subsemigroups.27 pages, Standard LaTeX with AmS fontsFunctional AnalysisAlgebraic GeometryDifferential GeometryHigh Energy Physics - TheoryQuantum Algebratext