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Ideals and congruence relations in lattices. (English) Zbl 0085.02002


MSC:

06B10 Lattice ideals, congruence relations
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[1] Г. Я. Арешкин, Об отношениях конгруенции в дистрибутивных структурах с нулевым элементом, ДАН СССР,90 (1953), pp. 485–486. · JFM 29.0452.02
[2] G. Birkhoff,Lattice theory (New York, 1948). · Zbl 0033.10103
[3] R. P. Dilworth, The structure of relatively complemented lattices,Annals of Math.,51 (1950), pp. 348–359. · Zbl 0036.01802
[4] R. P. Dilworth andM. Hall, The imbedding problem for modular lattices,Annals of Math.,45 (1944), pp. 450–456. · Zbl 0060.06102
[5] N. Funayama andT. Nakayama, On the distributivity of a lattice of lattice-congruences,Proc. Imp. Acad. Tokyo,18 (1942), pp. 553–554. · Zbl 0063.01483
[6] G. Grätzer andE. T. Schmidt, Hálók ideáljai és kongruenciarelációi. I,MTA Mat. és Fiz. Oszt. Közl.,7 (1957), pp. 93–108.
[7] G. Grätzer andE. T. Schmidt, Hálók ideáljai és kongruenciarelációi. II,MTA Mat. és Fiz. Oszt. Közl.,7 (1957), pp. 417–434.
[8] G. Grätzer andE. T. Schmidt, Hálók ideáljai és kongruenciarelációi. III,MTA Mat. és Fiz. Oszt. Közl.,8 (1958) (under press).
[9] G. Grätzer andE. T. Schmidt, On ideal theory for lattices,Acta Sci. Math. Szeged,19 (1958), pp. 82–92. · Zbl 0092.26802
[10] G. Grätzer andE. T. Schmidt, On the Jordan–Dedekind chain condition,Acta Sci. Math. Szeged,18 (1957), pp. 52–56. · Zbl 0079.04501
[11] G. Grätzer andE. T. Schmidt, Characterizations of relatively complemented distributive lattices,Publ. Math. Debrecen,5 (1958), pp. 275–287. · Zbl 0080.25402
[12] G. Grätzer andE. T. Schmidt, Two notes on lattice congruences,Annales Univ. Sci. Budapestiensis de Rolando Eötvös nominatae, Sectio Math.,1 (1958) (under press). · Zbl 0089.25603
[13] J. Hashimoto, Direct, subdirect decompositions and congruence relations,Osaka Math. Journal,9 (1957), pp. 87–112. · Zbl 0078.01805
[14] J. Hashimoto, Ideal theory for lattices,Math. Japonicae,2 (1952), pp. 149–186. · Zbl 0048.25903
[15] J. Jakubik, Relàcie kongruentnosti a slabá projektivnosť vo sväzoch,Časopis Pěst. Mat.,80 (1955), pp. 206–216.
[16] M. Kolibiar, O kongruenciách na distributivnych sväzoch,Acta Facultatis Rev. Nat. Univ. Comenianae, Math.,1 (1956), pp. 247–253.
[17] O. Ore, Theory of equivalence relations,Duke Math. Journal,9 (1942), pp. 573–627. · Zbl 0060.06201
[18] T. Tanaka, Canonical subdirect factorizations of lattices,J. Sci. Hiroshima Univ., Ser. A,16 (1952), pp. 239–246. · Zbl 0049.01704
[19] H. Wallman, Lattices and topological spaces,Annals of Math.,39 (1938), pp. 112–126. · Zbl 0018.33202
[20] Shih-chiang Wang, Notes on the permutability of congruence relations,Acta Math. Sinica,3 (1953), pp. 133–141. · Zbl 0099.26101
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