Geodesic
Characterizations for Prime Semilattices
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1059-1073

Voir la notice de l'article provenant de la source Cambridge University Press

Throughout this paper when we refer to a semilattice S we shall mean that S is a meet semilattice. We shall denote the infimum of two elements a, b of S by a ∧ b, and the supremum, if it exists, by a ∨ b. A prime semilattice is a meet semilattice such that the infimum distributes over all existing finite suprema, in the sense that if x 1 ∨ x 2 ... ∨ xn exists then (x ∧ x 1) ∨ (x ∧ x 2) ... ∨ (x ∧ xn ) exists for any x and equals x ∧ (x 1 ∨ x 2 ... ∨ xn ). Such semilattices were first studied by Balbes [1]and we use his terminology.A non-empty subset F of S is a filter provided that x ∧ y ∊ F if and only if x ∊ F and y ∊ F. 
Shum, K. P.; Chan, M. W.; Lai, C. K.; So, K. Y. Characterizations for Prime Semilattices. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1059-1073. doi: 10.4153/CJM-1985-057-4
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