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A regular hypersubstitution is a mapping which takes every $n_i$-ary operation symbol to an $n_i$-ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show...
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