Some comments and examples on generation of (hyper-)archimedean -groups and -rings
This paper systematizes some theory concerning the generation of -groups and reduced -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 -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...