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Infinite joins that are finitely join-irreducible. (English) Zbl 0793.06005

Summary: Complete lattices are studied which contain an element \(u\) which is not the join of a finite set of smaller elements, but is the join of all elements \(<u\).

MSC:

06B23 Complete lattices, completions
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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References:

[1] George M.Bergman and FredGalvin (1987) Transversals of families in complete lattices, and torsion in product modules, Order 3, 391-403. · Zbl 0597.06003 · doi:10.1007/BF00340781
[2] Kenneth R.Goodearl and BirgeZimmermann-Huisgen (1986) Boundedness of direct products of torsion modules, J. Pure & Applied Algebra 39, 251-273. · Zbl 0581.16001 · doi:10.1016/0022-4049(86)90146-5
[3] BirgeZimmermann-Huisgen (1988) Transversally bounded lattices, Order 5, 187-207. · Zbl 0658.06002 · doi:10.1007/BF00337623
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