Hopfian $\ell$-groups, MV-algebras and AF~{C}*-algebras
Daniele Mundici · Forum Mathematicum · 2016
Abstract An algebra is said to be hopfian if it is not isomorphic to a proper quotient of itself. We describe several classes of hopfian and of non-hopfian unital lattice-ordered abelian groups and MV-algebras. Using Elliott classification and K 0 ${K_{0}}$ -theory, we apply our results to other related structures, notably the Farey–Stern–Brocot AF C * ${\mathrm{C}^{*}}$ -algebra and all its primitive quotients, including the Behnke–Leptin C * ${\mathrm{C}^{*}}$ -algebras 𝒜 k , q ${\mathcal{A}_{k,q}}$ .