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Irreducible elements of posets. (English) Zbl 1039.06002

Summary: Join- (meet-, resp.) irreducible elements of posets are defined and their connection with the weakly dense subsets is studied. Especially, the weak separability of posets of finite length is found.

MSC:

06A06 Partial orders, general
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References:

[1] Birkhoff G.: Lattice Theory. 3rd, Providence, Rhode Island, 1967. · Zbl 0153.02501
[2] Kelly D., Trotter W. T., Jr.: Dimension theory for ordered sets. Ordered sets, Proc. NATO Adv. Study Inst. Banff I. Rival, 1981, 171-211.
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[5] Šešelja B., Tepavčević A.: On generation of fìnite posets by meet-irreducibles. Diskrete Math. 186 (1998), 269-275. · Zbl 0952.06002 · doi:10.1016/S0012-365X(97)00196-9
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