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

Abstract

Let denote the two element Boolean algebra and be the semimodule of all n-square symmetric Boolean matrices with zero diagonal. We characterize (i) subsemimodules of whose nonzero members all have factor rank 2, (ii) linear mappings from to that send distinct elements of term rank 2 to distinct elements of factor rank 2 and (iii) linear mappings from to that preserve elements of factor rank 2 and also elements of factor rank k for some

Keywords:

• semimodule
• Boolean symmetric matrix
• factor rank
• term rank
• linear mapping

AMS Subject Classifications:

• 15A86
• 15A03
• 15A04

Acknowledgement

The research of the first author was supported by the University of Malaya Research Grant RG157-11AFR.