A Note on Commutative l-Groups
1971 ◽
Vol 12
(1)
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pp. 69-74
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Keyword(s):
Let G be a commutative lattice ordered group. Theorem 1 gives necessary and sufficient conditions under which a⊥ with a∈G is a maximal l-ideal. A wide family of, l-groups G having the property that the orthogonal complement of each atom is a maximal l-ideal is described. Conditionally σ-complete and hence conditionally complete vector lattices belong to the family.It follows immediately that if a is an atom in a conditionally complete vector lattice then a⊥ is a maximal vector lattice ideal. This theorem has been proved in [7] by Yamamuro. Theorem 2 generalizes another result contained in [7]. Namely we prove that if M is a closed maximal l-ideal of an archimedean l-group G then there exists an atom a ∈ G such that M = a⊥.
1971 ◽
Vol 5
(3)
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pp. 331-335
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Keyword(s):
1968 ◽
Vol 20
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pp. 1136-1149
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Keyword(s):
1968 ◽
Vol 20
◽
pp. 1362-1364
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Keyword(s):
1992 ◽
Vol 15
(1)
◽
pp. 65-81
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2012 ◽
Vol 05
(03)
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pp. 1250045
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