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Zbl 0706.06002
Abian, Alexander; Amin, Wael A.
Existence of prime ideals and ultrafilters in partially ordered sets. (English)
[J] Czech. Math. J. 40(115), No.1, 159-163 (1990). ISSN 0011-4642; ISSN 1572-9141/e

In the existing literature the algebraic notions of an ideal and a prime ideal and the corresponding dual notions of a filter and an ultrafilter are predominantly generalized to the case of lattices [{\it G. Birkhoff}: Lattice theory. Corr. repr. of the 1967 3rd ed. (1979; Zbl 0505.06001); and {\it G. Grätzer}: General lattice theory (1978; Zbl 0436.06001)]. Here the authors introduce these notions in partially ordered sets. An ideal in a partially ordered set can be defined in various (not necessarily pairwise equivalent) ways. The same is the case for the definitions of a prime ideal, a filter and an ultrafilter.
[R.A.Alo]

MSC 2000:: *06A06 Partial order

Keywords: prime ideal; filter; ultrafilter

Citations: Zbl 0505.06001; Zbl 0436.06001

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