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We show how the existence of various free vector lattices and free vectorlattice algebras can be derived from a theorem on equational classes inuniversal algebra. A discussion about free $f$-algebras over non-empty sets isgiven, where the main issues appear to be open. It is indicated how theexistence results for free vector lattices and vector lattice algebras can beused for easy proofs of existence results for free Banach lattices and freeBanach lattice algebras. A detailed exposition of the necessary material fromuniversal algebra is included.

Free vector lattices and free vector lattice algebras