Semimodules and preservers of traceless symmetric Boolean matrices of factor rank two.

Letdenote the two element Boolean algebra andbe the semimodule of alln-square symmetric Boolean matrices with zero diagonal. We characterize (i) subsemimodules ofwhose nonzero members all have factor rank 2, (ii) linear mappings fromtothat send distinct elements of term rank 2 to distinct elements of factor rank 2 and (iii) linear mappings fromtothat preserve elements of factor rank 2 and also elements of factor rankkfor some [ABSTRACT FROM PUBLISHER]