Ordered groups with greatest common divisors theory
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...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200004087 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |