sentences:  Maximal regular bands need not to be closed under formula_5 as defined; counterexamples are easily found using multiplicative rectangular bands.These cases are closed, however, under the cubic variant of formula_5 defined by formula_223 since in these cases formula_224 reduces to formula_225 to give the dual rectangular band.By replacing the condition of regularity by normality formula_226, every maximal normal multiplicative band formula_17 in formula_202 is also closed under formula_229 with formula_230, where formula_231, forms a Boolean skew lattice.