Almost ff-universal and q-universal varieties of modular 0-lattices

V. Koubek; J. Sichler

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On modular elements of the lattice of semigroup varieties

Boris M. Vernikov (2007)

Commentationes Mathematicae Universitatis Carolinae

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A semigroup variety is called if it is a modular element of the lattice of all semigroup varieties. We obtain a strong necessary condition for a semigroup variety to be modular. In particular, we prove that every modular nil-variety may be given by 0-reduced identities and substitutive identities only. (An identity $u = v$ is called if the words $u$ and $v$ depend on the same letters and $v$ may be obtained from $u$ by renaming of letters.) We completely determine all commutative modular varieties...