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On the Embedding into a Ring of an Archimedean ι-Group

Published online by Cambridge University Press:  20 November 2018

Anthony W. Hager  and
Lewis C. Robertson
Anthony W. Hager
Affiliation:
Wesley an University, Middletown, Connecticut
Lewis C. Robertson
Affiliation:
Wesley an University, Middletown, Connecticut
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We shall prove the following about the “ringification” ρA of [2] and [5] of an archimedean l-group A: (a) Any “minimal ring” containing A is ρA; (b) A ↦ ρA is a reflector; (c) ρA need not be laterally complete when A is. These constitute the solutions to the problems posed in [2] by Paul Conrad.

1. The embedding into a ring. Let be the category which has objects archimedean l-groups A with distinguished positive weak unit eA, and morphisms l-group homomorphisms h: A → B with h(eA) = eB. Let be the category with objects archimedean f-rings R with identity 1R which is a weak unit, and morphisms l-ring homomorphisms h: R → S with h(lR) = 1S.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 1 - 8
Copyright
Copyright © Canadian Mathematical Society 1979

References

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