Ordered groups with greatest common divisors theory
2000 ◽
Vol 24
(7)
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pp. 469-479
An embedding (called aGCD theory) of partly ordered abelian groupGinto abelian l-groupΓis investigated such that any element ofΓis an infimum of a subset (possible non-finite) fromG. It is proved that a GCD theory need not be unique. Acomplete GCD theoryis introduced and it is proved thatGadmits a complete GCD theory if and only if it admits a GCD theoryG→Γsuch thatΓis an Archimedean l-group. Finally, it is proved that a complete GCD theory is unique (up too-isomorphisms) and that a po-group admits the complete GCD theory if and only if anyv-ideal isv-invertible.
1972 ◽
Vol 18
(1)
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pp. 81-83
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1975 ◽
Vol 19
(1)
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pp. 62-73
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2021 ◽
Vol 13
(1)
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pp. 182-191
1994 ◽
Vol 14
(2)
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pp. 130-138
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1995 ◽
Vol 44
(2)
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pp. 395-402
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