Inverse Semigroups of Bicongruences on Algebras, Particularly Semilattices
Isomorphisms between quotient algebras of an algebra make up an inverse semigroup which carries information about the algebra. The extent of this information is explored in the case of semilattices; the main result is that any (meet) semilattice admitting no joins of incomparable elements, and satisfying chain conditions, is determined up to isomorphism by the inverse semigroup of isomorphisms between its quotient semilattices.
KeywordsInverse Semigroup Universal Algebra Congruence Lattice Subdirect Product Inverse Monoids
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