Ordered groups with greatest common divisors theory

Jiří Močkoř

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 24, 1-11

Abstract:

An embedding (called a GCD theory ) of partly ordered abelian group G into abelian l-group Γ is investigated such that any element of Γ is an infimum of a subset (possible non-finite) from G . It is proved that a GCD theory need not be unique. A complete GCD theory is introduced and it is proved that G admits a complete GCD theory if and only if it admits a GCD theory G → Γ such that Γ is an Archimedean l-group. Finally, it is proved that a complete GCD theory is unique (up to o -isomorphisms) and that a po-group admits the complete GCD theory if and only if any v -ideal is v -invertible.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:464297

DOI: 10.1155/S0161171200004087

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