Abstract:
The question about the structure
of lattices of subclasses of various classes of
algebras is one of the basic ones in universal algebra. The case
under consideration most frequently concerns lattices of
subvarieties (subquasivarieties) of varieties (quasivarieties) of
universal algebras. A similar question is also meaningful for other
classes of algebras, in particular, for universal classes of
algebras. The union of two $\forall$-classes is itself a
$\forall$-class, hence such lattices are distributive. As a rule,
those lattices of subclasses are rather large and are not simply
structured. In this connection, it is of interest to distinguish
some sublattices of such lattices that would model certain
properties of the lattices themselves. The present paper deals with
a similar problem for $\forall$-classes and varieties of universal
algebras.
Keywords:$\forall$-class of universal algebras, variety
of universal algebras, lattice of subclasses of class of algebras.
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