Known and new methods of decomposing a boolean relation are presented together with methods of making the decomposition visible.Homogeneous and heterogeneous relations are handled with non-iterative as well as iterative methods. Such aspects as reducibility,cyclicity,primitivity,difunctionality, Ferrer s re- lations,Moore-Penrose inverses,independence and line-covering, chainability, game decompositions,matchings,Hall conditions,term rank,chainability, full indecomposability,and others are handled under one common roof. We have also tried to collect several concepts for nonnegative real-valued matri- ces and to treat them as concepts for boolean matrices. An additional impetus for this study was to give all this a relation algebraic basis avoiding counting arguments.Several proofs of already known facts are, therefore, quite different from the classical ones.     «

Known and new methods of decomposing a boolean relation are presented together with methods of making the decomposition visible.Homogeneous and heterogeneous relations are handled with non-iterative as well as iterative methods. Such aspects as reducibility,cyclicity,primitivity,difunctionality, Ferrer s re- lations,Moore-Penrose inverses,independence and line-covering, chainability, game decompositions,matchings,Hall conditions,term rank,chainability, full indecomposability,and others are handl...    »