Abstract
Let variety μ be given by the balanced identities of signature Ω not containing unary operations. Then, in the lattice of subvarieties of variety μ, any element different from μ has an element covering it. In particular, variety μ might be the varieties of semigroups, groupoids, n-associatives, etc. It is also proven that, in the lattice of varieties of semigroups, there exists an element having a continuum of covering elements.
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