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Hager, A. W.; Johnson, D. G.
Some comments and examples on generation of (hyper-)archimedean $\ell $-groups and $f$-rings. Annales de la faculté des sciences de Toulouse Mathématiques, Sér. 6, 19 no. S1 (2010), p. 75-100
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This paper systematizes some theory concerning the generation of $\ell $-groups and reduced $f$-rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an $\ell $-group, or an identity to an $f$-ring and find significant contrasts between these cases. In $\ell $-groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by a basic example of Conrad and Martinez which we revisit and elaborate. For reduced $f$-rings, on the other hand, these properties do inherit upwards.
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