×

zbMATH — the first resource for mathematics

On the structure of lattices in which every element is a join of join-irreducible elements. (English) Zbl 0484.06008

MSC:
06B10 Lattice ideals, congruence relations
06B05 Structure theory of lattices
06C10 Semimodular lattices, geometric lattices
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] G. Birkhoff andO. Frink, Representation of lattices by sets,Trans. Amer. Math. Soc. 64 (1948), 299–316.MR 10–279 · Zbl 0032.00504 · doi:10.1090/S0002-9947-1948-0027263-2
[2] P. Crawley andR. P. Dilworth,Algebraic theory of lattices, Prentice-Hall, Englewood Cliffs (N. J.), 1973. · Zbl 0494.06001
[3] G. Grätzer,General lattice theory Birkhäuser, Basel, 1978.MR 80 c:06001a
[4] G. Grätzer andE. T. Schmidt, On inaccessible and minimal congruence relations, I,Acta Sci. Math. (Szeged)21 (1960), 337–342.MR 23 # A3697 · Zbl 0099.01903
[5] R. Fritzsche,Beitrag zur Theorie der zyklisch erzeugten modularen Verbände, Universität Halle, 1978. (Doctoral thesis)
[6] F. Maeda andSh. Maeda,Theory of symmetric lattices, Springer, Berlin, 1970.MR 44 # 123 · Zbl 0219.06002
[7] G. Richter,Tur Theorie der zyklisch erzeugten modularen Verbände, Universität Halle, 1975. (Doctoral thesis)
[8] G. Richter, Strong purity in lattices,Beiträge zur Algebra und Geometrie,12 (1981).
[9] G. Richter andM. Stern, A unified theory of cyclically generated modular lattices andAC-lattices,Studia Sci. Math. Hungar. 11 (1976), 413–429. · Zbl 0432.06004
[10] G. Richter andM. Stern,ZI-lattices,Proc. Colloq. on Universal Algebra, Model Theory and Lattice Theory (held in Esztergom, 1977), North Holland, Amsterdam, 1982, 635–652.
[11] E. T. Schmidt, On the characterization of the congruence lattice of lattices,Proc. Lattice Theory Conf. (held in Ulm, 1975), 162–179.Zbl 376. 06008
[12] M. Stern, Baer lattices, I,Wiss. Z. M.-Luther-Univ. Halle–Wittenberg Math.-Natur Reihe 27/4 (1978), 135–140.MR 80 k:06007
[13] M. Stern, Baer lattices. II,Wiss. Z. M.-Luther-Univ. Halle–Wittenberg Math.-Natur. Reihe 27/5 (1978), 65–69.MR 80 e:06003a
[14] M. Stern, Baer lattices, III,Wiss. Z. M.-Luther-Univ. Halle–Wittenberg Math.-Natur. Reihe 28/1 (1979), 21–24.MR 80 e:06003b
[15] M. Stern,Baersche Verbände, Universität Halle, 1978. (Doctoral thesis)
[16] M. Stern, Generalized matroid lattices,Algebraic methods in graph theory (Colloq. Math. Soc. J. Bolyai, 25;held in Szeged, 1978), North-Holland, Amsterdam, 1981, 727–748.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.