Hopfian $\ell$-groups, MV-algebras and AF C$^*$-algebras
Daniele Mundici

TL;DR
This paper investigates hopfian properties of unital lattice-ordered abelian groups and MV-algebras, applying classification theories to connect these properties with AF C*-algebras and their quotients.
Contribution
It characterizes hopfian and non-hopfian classes of these algebraic structures and links them to AF C*-algebras using K-theory and Elliott classification.
Findings
Identifies classes of hopfian and non-hopfian MV-algebras and lattice-ordered groups.
Connects hopfian properties to AF C*-algebras via K-theory.
Analyzes primitive quotients of Farey-Stern-Brocot AF C*-algebra.
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 -theory, we apply our results to other related structures, notably the Farey-Stern-Brocot AF C-algebra and all its primitive quotients, including the Behnke-Leptin C-algebras .
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Fuzzy and Soft Set Theory
