latticeembedded
Latticeembedded is a term used to describe the embedding of one lattice into another lattice, preserving the lattice operations. In mathematics, a lattice is a partially ordered set in which any two elements have a greatest lower bound (meet) and a least upper bound (join), usually denoted ∧ and ∨. A lattice embedding is an injective function f from a lattice L into a lattice M that preserves both operations: for all a,b in L, f(a ∨ b) = f(a) ∨ f(b) and f(a ∧ b) = f(a) ∧ f(b). Equivalently, a lattice embedding is an order-embedding, meaning a ≤ b in L if and only if f(a) ≤ f(b) in M.
A lattice embedding need not be onto; its image is a sublattice of M that is lattice-isomorphic
Lattice embeddings play a role in several areas. In universal algebra, they help study sublattices and substructures.