Lattice Characteristics of Classes of Semigroups
We say that a class A of semigroups is lattice-characterized if one can indicate conditions formulated in lattice-theoretic terms such that the lattice SubS of a semigroup S satisfies these conditions if and only if S ∈ A; such conditions will be called a lattice characteristic of a class A. Speaking about lattice-theoretic conditions, we mean abstract properties (i.e. inherited by isomorphic images) so each lattice-characterized class is clearly abstract. If all semigroups in such a class A are isomorphic, i.e., in other words, A consists, up to isomorphism, of a single semigroup, say A, then we say that the semigroup A is lattice-characterized.
KeywordsLattice Characteristic Finite Order Infinite Order Semi Group Finite Semigroup
Unable to display preview. Download preview PDF.