Bergman, George M.; Zimmermann-Huisgen, Birge Infinite joins that are finitely join-irreducible. (English) Zbl 0793.06005 Order 7, No. 1, 27-40 (1990). 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 \(<u\). Cited in 2 Documents MSC: 06B23 Complete lattices, completions 06A15 Galois correspondences, closure operators (in relation to ordered sets) Keywords:finitely join-irreducible element; nonprincipal maximal ideal; Boolean ring of subsets; closure operator; upward and downward generating numbers PDFBibTeX XMLCite \textit{G. M. Bergman} and \textit{B. Zimmermann-Huisgen}, Order 7, No. 1, 27--40 (1990; Zbl 0793.06005) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.