Prime and maximal ideals of partially ordered sets
Mathematica Slovaca (2006)
- Volume: 56, Issue: 1, page 1-22
- ISSN: 0139-9918
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topErné, Marcel. "Prime and maximal ideals of partially ordered sets." Mathematica Slovaca 56.1 (2006): 1-22. <http://eudml.org/doc/32126>.
@article{Erné2006,
author = {Erné, Marcel},
journal = {Mathematica Slovaca},
keywords = {Boolean algebra; down-set; prime ideal; maximal ideal; pseudocomplement; semidistributive},
language = {eng},
number = {1},
pages = {1-22},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Prime and maximal ideals of partially ordered sets},
url = {http://eudml.org/doc/32126},
volume = {56},
year = {2006},
}
TY - JOUR
AU - Erné, Marcel
TI - Prime and maximal ideals of partially ordered sets
JO - Mathematica Slovaca
PY - 2006
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 56
IS - 1
SP - 1
EP - 22
LA - eng
KW - Boolean algebra; down-set; prime ideal; maximal ideal; pseudocomplement; semidistributive
UR - http://eudml.org/doc/32126
ER -
References
top- ALEXANDROFF P., Diskrete Räume, Mat. Sb. 2 (1937), 501-518. (1937) Zbl0018.09105MR0004764
- BANASCHEWSKI B.-ERNÉ M., On Krull's separation lemma, Order 10 (1993), 253-260. (1993) Zbl0795.06005MR1267191
- BIRKHOFF G., Lattice Theory, (3rd ed.). Amer. Math. Soc .Colloq. Publ. 25, Amer. Math. Soc., Providence, RI, 1979. (1979) Zbl0505.06001MR0598630
- DAVID E.-ERNÉ M., Ideal completion and Stone representation of ideal-distributive ordered sets, Topology Appl. 44 (1992), 95-113. (1992) Zbl0768.06003MR1173247
- DAVEY B. A.-PRIESTLEY H. A., Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990. (1990) Zbl0701.06001MR1058437
- ERNÉ M., Distributivgesetze und Dedekindsche Schnitte, Abh. Braunschw. Wiss. Ges. 33 (1982), 117-145. (1982) MR0693169
- ERNÉ M., Bigeneration in complete lattices and principal separation in partially ordered sets, Order 8 (1991), 197-221. (1991) MR1137911
- ERNÉ M., Semidistributivity, prime ideals, and the subbase lemma, Rend. Circ. Mat. Palermo (2) 41 (1992), 241-250. (1992) Zbl0779.06001MR1196618
- ERNÉ M., Distributive laws for concept lattices, Algebra Universalis 30 (1993), 538-580. (1993) Zbl0795.06006MR1240572
- ERNÉ M., Prime ideal theorems and systems of finite character, Comment. Math. Univ. Carolin. 38 (1997), 513-536. (1997) Zbl0938.03072MR1485072
- ERNÉ M., Prime ideal theory for general algebras, Appl. Categ. Structures 8 (2000), 115-144. Zbl0980.08001MR1785840
- ERNÉ M.-WILKE G., Standard completions for quasiordered sets, Semigroup Forum 27 (1983), 351-376. (1983) Zbl0517.06009MR0714681
- FRINK O., Ideals in partially ordered sets, Amer. Math. Monthly 61 (1954), 223-234. (1954) Zbl0055.25901MR0061575
- FRINK O., Pseudo-complements in semi-lattices, Duke Math. J. 29 (1962), 505-514. (1962) Zbl0114.01602MR0140449
- GANTER B.-WILLE R., Formal Concept Analysis - Mathematical Foundation, Springer-Verlag, Berlin-Heidelberg-New York, 1999. (1999) MR1707295
- 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. Zbl1088.06001MR1975381
- GORBUNOV A. V.-TUMANOV V. L., On the existence of prime ideals in semidistributive lattices, Algebra Universalis 16 (1983), 250-252. (1983) Zbl0516.06006MR0692266
- GRÄTZER G., General Lattice Theory, Birkhäuser, Basel, 1973. (1973)
- 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. (1967) MR0284328
- HERRLICH H., The axiom of choice holds if and only if maximal closed filters exist, MLQ Math. Log. Q. 49 (2003), 323-324. MR1979139
- HOWARD P.-RUBIN J. E., Consequences of the Axiom of Choice, Math. Surveys Monogr. 59, Amer. Math. Soc, Providence, RI, 1998. (1998) Zbl0947.03001MR1637107
- JOHNSTONE P. T., Almost maximal ideals, Fund. Math. 123 (1984), 201-206. (1984) Zbl0552.06004MR0761975
- KATRIŇÁK T., Pseudokomplementare Halbverbande, Mat. Casopis 18 (1968), 121-143. (1968) MR0262123
- KATRIŇÁK T., The structure of distributive p-algebras. Regularity and congruences, Algebra Universalis 3 (1973), 238-246. (1973) MR0332598
- KATRIŇÁK T., A new proof of the Glivenko-Frink Theorem, Bull. Soc Roy. Sci. Liege 50 (1981), 171. (1981) Zbl0482.06001MR0646688
- LARMEROVÁ J.-RACHŮNEK J., Translations of distributive and modular ordered sets, Acta Univ. Palack. Olomuc. Fac. Rerum. Natur. Math. 27 (1988), 13-23. (1988) Zbl0693.06003MR1039879
- NIEDERLE J., Boolean and distributive ordered sets: characterization and representation by sets, Order 12 (1995), 189-210. (1995) Zbl0838.06004MR1354802
- 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. MR1949661
- RUBIN H.-SCOTT D., Some topological theorems equivalent to the Boolean prime ideal theorem, Bull. Amer. Math. Soc. 60 (1954), 389. (1954)
- SCOTT D., The theorem on maximal ideals in lattices and the axiom of choice, Bull. Amer. Math. Soc. 60 (1954), 83. (1954)
- TARSKI A., Prime ideal theorems for Boolean algebras and the axiom of choice, Bull. Amer. Math. Soc. 60 (1954), 390-391 (Abstract). (1954)
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