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Some comments and examples on generation of (hyper-)archimedean -groups and f -rings

A. W. HagerD. G. Johnson — 2010

Annales de la faculté des sciences de Toulouse Mathématiques

This paper systematizes some theory concerning the generation of -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 -group, or an identity to an f -ring and find significant contrasts between these cases. In -groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by...

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