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arXiv · 1509.03230

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

Daniele Mundici
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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 $K_0$-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 $\mathcal A_{k,q}$.

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Daniele Mundici. 2015-09-10. Hopfian $\ell$-groups, MV-algebras and AF C$^*$-algebras. https://arxiv.org/abs/1509.03230

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