Mapping Abelian \(\ell\)-groups with strong unit one-one into MV algebras
An Abelian \(\ell\)-group (i.e., lattice-ordered group) G is said to have a strong unit u provided \(u\in G^+\) and to every element \(g\in G\) corresponds a natural number n such that \(g\leq nu\). Abelian \(\ell\)-groups with strong unit are important in the theory of \(C^*\)-algebras. MV- algebras, invented by C. C. Chang, are an algebraic counterpart of the \(\aleph_ 0\)-valued Lukasiewicz sentential calculus. Based on these facts and a remark of Dieudonné to the effect that ''invention of functors is one of the main goals of modern mathematics'', the author constructs an object-injective functor from the category of Abelian \(\ell\)-groups with strong unit to the category of MV-algebras. Further results and applications are announced in a note added in proof.
\(\aleph _ 0\)-valued Lukasiewicz sentential calculus
scientific article; zbMATH DE number 3926994
scientific article