  Various 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.
