| Title:
|
Prime and maximal ideals of partially ordered sets (English) |
| Author:
|
Erné, Marcel |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
1-22 |
| . |
| Category:
|
math |
| . |
| MSC:
|
03E25 |
| MSC:
|
06A06 |
| idZBL:
|
Zbl 1164.03011 |
| idMR:
|
MR2217576 |
| . |
| Date available:
|
2009-09-25T14:29:31Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/131102 |
| . |
| Reference:
|
[1] ALEXANDROFF P.: Diskrete Räume.Mat. Sb. 2 (1937), 501-518. Zbl 0018.09105, MR 0004764 |
| Reference:
|
[2] BANASCHEWSKI B.-ERNÉ M.: On Krull's separation lemma.Order 10 (1993), 253-260. Zbl 0795.06005, MR 1267191 |
| Reference:
|
[3] BIRKHOFF G.: Lattice Theory.(3rd ed.). Amer. Math. Soc .Colloq. Publ. 25, Amer. Math. Soc., Providence, RI, 1979. Zbl 0505.06001, MR 0598630 |
| Reference:
|
[4] DAVID E.-ERNÉ M.: Ideal completion and Stone representation of ideal-distributive ordered sets.Topology Appl. 44 (1992), 95-113. Zbl 0768.06003, MR 1173247 |
| Reference:
|
[5] DAVEY B. A.-PRIESTLEY H. A.: Introduction to Lattices and Order.Cambridge University Press, Cambridge, 1990. Zbl 0701.06001, MR 1058437 |
| Reference:
|
[6] ERNÉ M.: Distributivgesetze und Dedekindsche Schnitte.Abh. Braunschw. Wiss. Ges. 33 (1982), 117-145. MR 0693169 |
| Reference:
|
[7] ERNÉ M.: Bigeneration in complete lattices and principal separation in partially ordered sets.Order 8 (1991), 197-221. MR 1137911 |
| Reference:
|
[8] ERNÉ M.: Semidistributivity, prime ideals, and the subbase lemma.Rend. Circ. Mat. Palermo (2) 41 (1992), 241-250. Zbl 0779.06001, MR 1196618 |
| Reference:
|
[9] ERNÉ M.: Distributive laws for concept lattices.Algebra Universalis 30 (1993), 538-580. Zbl 0795.06006, MR 1240572 |
| Reference:
|
[10] ERNÉ M.: Prime ideal theorems and systems of finite character.Comment. Math. Univ. Carolin. 38 (1997), 513-536. Zbl 0938.03072, MR 1485072 |
| Reference:
|
[11] ERNÉ M.: Prime ideal theory for general algebras.Appl. Categ. Structures 8 (2000), 115-144. Zbl 0980.08001, MR 1785840 |
| Reference:
|
[12] ERNÉ M.-WILKE G.: Standard completions for quasiordered sets.Semigroup Forum 27 (1983), 351-376. Zbl 0517.06009, MR 0714681 |
| Reference:
|
[13] FRINK O.: Ideals in partially ordered sets.Amer. Math. Monthly 61 (1954), 223-234. Zbl 0055.25901, MR 0061575 |
| Reference:
|
[14] FRINK O.: Pseudo-complements in semi-lattices.Duke Math. J. 29 (1962), 505-514. Zbl 0114.01602, MR 0140449 |
| Reference:
|
[15] GANTER B.-WILLE R.: Formal Concept Analysis - Mathematical Foundation.Springer-Verlag, Berlin-Heidelberg-New York, 1999. MR 1707295 |
| Reference:
|
[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. Zbl 1088.06001, MR 1975381 |
| Reference:
|
[17] GORBUNOV A. V.-TUMANOV V. L.: On the existence of prime ideals in semidistributive lattices.Algebra Universalis 16 (1983), 250-252. Zbl 0516.06006, MR 0692266 |
| Reference:
|
[18] GRÄTZER G.: General Lattice Theory.Birkhäuser, Basel, 1973. |
| Reference:
|
[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 0284328 |
| Reference:
|
[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 1979139 |
| Reference:
|
[21] HOWARD P.-RUBIN J. E.: Consequences of the Axiom of Choice.Math. Surveys Monogr. 59, Amer. Math. Soc, Providence, RI, 1998. Zbl 0947.03001, MR 1637107 |
| Reference:
|
[22] JOHNSTONE P. T.: Almost maximal ideals.Fund. Math. 123 (1984), 201-206. Zbl 0552.06004, MR 0761975 |
| Reference:
|
[23] KATRIŇÁK T.: Pseudokomplementare Halbverbande.Mat. Casopis 18 (1968), 121-143. MR 0262123 |
| Reference:
|
[24] KATRIŇÁK T.: The structure of distributive p-algebras. Regularity and congruences.Algebra Universalis 3 (1973), 238-246. MR 0332598 |
| Reference:
|
[25] KATRIŇÁK T.: A new proof of the Glivenko-Frink Theorem.Bull. Soc Roy. Sci. Liege 50 (1981), 171. Zbl 0482.06001, MR 0646688 |
| Reference:
|
[26] LARMEROVÁ J.-RACHŮNEK J.: Translations of distributive and modular ordered sets.Acta Univ. Palack. Olomuc. Fac. Rerum. Natur. Math. 27 (1988), 13-23. Zbl 0693.06003, MR 1039879 |
| Reference:
|
[27] NIEDERLE J.: Boolean and distributive ordered sets: characterization and representation by sets.Order 12 (1995), 189-210. Zbl 0838.06004, MR 1354802 |
| Reference:
|
[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 1949661 |
| Reference:
|
[29] RUBIN H.-SCOTT D.: Some topological theorems equivalent to the Boolean prime ideal theorem.Bull. Amer. Math. Soc. 60 (1954), 389. |
| Reference:
|
[30] SCOTT D.: The theorem on maximal ideals in lattices and the axiom of choice.Bull. Amer. Math. Soc. 60 (1954), 83. |
| Reference:
|
[31] TARSKI A.: Prime ideal theorems for Boolean algebras and the axiom of choice.Bull. Amer. Math. Soc. 60 (1954), 390-391 (Abstract). |
| . |
