Voir la notice de l'article provenant de la source Czech Digital Mathematics Library
MR ZblErné, Marcel. Prime and maximal ideals of partially ordered sets. Mathematica slovaca, Tome 56 (2006) no. 1, pp. 1-22. http://geodesic.mathdoc.fr/item/MASLO_2006_56_1_a1/
@article{MASLO_2006_56_1_a1,
author = {Ern\'e, Marcel},
title = {Prime and maximal ideals of partially ordered sets},
journal = {Mathematica slovaca},
pages = {1--22},
year = {2006},
volume = {56},
number = {1},
mrnumber = {2217576},
zbl = {1164.03011},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MASLO_2006_56_1_a1/}
}
[1] ALEXANDROFF P.: Diskrete Räume. Mat. Sb. 2 (1937), 501-518. | MR | Zbl
[2] BANASCHEWSKI B.-ERNÉ M.: On Krull's separation lemma. Order 10 (1993), 253-260. | MR | Zbl
[3] BIRKHOFF G.: Lattice Theory. (3rd ed.). Amer. Math. Soc .Colloq. Publ. 25, Amer. Math. Soc., Providence, RI, 1979. | MR | Zbl
[4] DAVID E.-ERNÉ M.: Ideal completion and Stone representation of ideal-distributive ordered sets. Topology Appl. 44 (1992), 95-113. | MR | Zbl
[5] DAVEY B. A.-PRIESTLEY H. A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge, 1990. | MR | Zbl
[6] ERNÉ M.: Distributivgesetze und Dedekindsche Schnitte. Abh. Braunschw. Wiss. Ges. 33 (1982), 117-145. | MR
[7] ERNÉ M.: Bigeneration in complete lattices and principal separation in partially ordered sets. Order 8 (1991), 197-221. | MR
[8] ERNÉ M.: Semidistributivity, prime ideals, and the subbase lemma. Rend. Circ. Mat. Palermo (2) 41 (1992), 241-250. | MR | Zbl
[9] ERNÉ M.: Distributive laws for concept lattices. Algebra Universalis 30 (1993), 538-580. | MR | Zbl
[10] ERNÉ M.: Prime ideal theorems and systems of finite character. Comment. Math. Univ. Carolin. 38 (1997), 513-536. | MR | Zbl
[11] ERNÉ M.: Prime ideal theory for general algebras. Appl. Categ. Structures 8 (2000), 115-144. | MR | Zbl
[12] ERNÉ M.-WILKE G.: Standard completions for quasiordered sets. Semigroup Forum 27 (1983), 351-376. | MR | Zbl
[13] FRINK O.: Ideals in partially ordered sets. Amer. Math. Monthly 61 (1954), 223-234. | MR | Zbl
[14] FRINK O.: Pseudo-complements in semi-lattices. Duke Math. J. 29 (1962), 505-514. | MR | Zbl
[15] GANTER B.-WILLE R.: Formal Concept Analysis - Mathematical Foundation. Springer-Verlag, Berlin-Heidelberg-New York, 1999. | MR
[16] GIERZ G.-HOFMANN K. H.-KEIMEL K.-LAWSON J. D.-MISLOVE M.-SCOTT D. S.: Continuous Lattices and Domains. Encyclopedia Math. Appl. 93, Cambridge University Press, Cambridge, 2003. | MR | Zbl
[17] GORBUNOV A. V.-TUMANOV V. L.: On the existence of prime ideals in semidistributive lattices. Algebra Universalis 16 (1983), 250-252. | MR | Zbl
[18] GRÄTZER G.: General Lattice Theory. Birkhäuser, Basel, 1973.
[19] HALPERN J.-LÉVY A.: The Boolean prime ideal theorem does not imply the axiom of choice. In: Axiomatic Set Theory. Proc Symp. Pure Math. Amer. Math. Soc University of California, Los Angeles, July 10-August 5, 1967 (D. Scott, ed.), Proc Sympos. Pure Math. 13, Amer. Math. Soc, Providence, RI, 1971, pp. 83-134. | MR
[20] HERRLICH H.: The axiom of choice holds if and only if maximal closed filters exist. MLQ Math. Log. Q. 49 (2003), 323-324. | MR
[21] HOWARD P.-RUBIN J. E.: Consequences of the Axiom of Choice. Math. Surveys Monogr. 59, Amer. Math. Soc, Providence, RI, 1998. | MR | Zbl
[22] JOHNSTONE P. T.: Almost maximal ideals. Fund. Math. 123 (1984), 201-206. | MR | Zbl
[23] KATRIŇÁK T.: Pseudokomplementare Halbverbande. Mat. Casopis 18 (1968), 121-143. | MR
[24] KATRIŇÁK T.: The structure of distributive p-algebras. Regularity and congruences. Algebra Universalis 3 (1973), 238-246. | MR
[25] KATRIŇÁK T.: A new proof of the Glivenko-Frink Theorem. Bull. Soc Roy. Sci. Liege 50 (1981), 171. | MR | Zbl
[26] LARMEROVÁ J.-RACHŮNEK J.: Translations of distributive and modular ordered sets. Acta Univ. Palack. Olomuc. Fac. Rerum. Natur. Math. 27 (1988), 13-23. | MR | Zbl
[27] NIEDERLE J.: Boolean and distributive ordered sets: characterization and representation by sets. Order 12 (1995), 189-210. | MR | Zbl
[28] RHINEGHOST Y. T.: The Boolean prime ideal theorem holds if and only if maximal open filters exist. Cah. Topol. Geom. Differ. Categ. 43 (2002), 313-315. | MR
[29] RUBIN H.-SCOTT D.: Some topological theorems equivalent to the Boolean prime ideal theorem. Bull. Amer. Math. Soc. 60 (1954), 389.
[30] SCOTT D.: The theorem on maximal ideals in lattices and the axiom of choice. Bull. Amer. Math. Soc. 60 (1954), 83.
[31] TARSKI A.: Prime ideal theorems for Boolean algebras and the axiom of choice. Bull. Amer. Math. Soc. 60 (1954), 390-391 (Abstract).