Splitting properties in Archimedean l-groups
1977 ◽
Vol 23
(2)
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pp. 247-256
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Throughout this paper an l-group will always mean an archimedean lattice-ordered group and we shall confine our attention to such groups. An l-group splits if it is a cardinal summand of each l-group that contains it as an l-ideal. Suppose that G is an l-subgroup of an l-group H. Then G is large in H or H is an essential extension of G if for each l-ideal L≠0 of H, L∩G≠0. G is essentially closed if it does not admit any proper essential extension. Conrad (1971) proved that each essentially closed l-group splits, but not conversely.
1971 ◽
Vol 5
(3)
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pp. 331-335
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Keyword(s):
1993 ◽
Vol 85
(1)
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pp. 1-20
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1992 ◽
Vol 116
(2)
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pp. 297-297
1991 ◽
Vol 70
(1-2)
◽
pp. 17-43
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Keyword(s):
1980 ◽
Vol 32
(4)
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pp. 924-936
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