Pacific Journal of Mathematics

Irreducible congruence relations on lattices.

D. T. Finkbeiner

Article information

Source
Pacific J. Math., Volume 10, Number 3 (1960), 813-821.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103038229

Mathematical Reviews number (MathSciNet)
MR0113817

Zentralblatt MATH identifier
0093.03901

Subjects
Primary: 06.00

Citation

Finkbeiner, D. T. Irreducible congruence relations on lattices. Pacific J. Math. 10 (1960), no. 3, 813--821. https://projecteuclid.org/euclid.pjm/1103038229


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References

  • [1] G. Birkhoff, Lattice Theory, Rev.ed. Amer. Math. Soc.Colloquium Publications, Vol. 25 (1948).
  • [2] R. P. Dilworth, The structure of relatively complemented lattices. Annals of Math,51, 1As the referee has pointed out,Lemma 4.1 expresses a property of the join irreduci- bles of any complete, distributive lattice which satisfies the descending chain condition.
  • [3] N. Funayama, and T. Takayama, On the distributivityof a lattice of congruence re- lations.Proc. Imp. Acad. Tokyo, 18 (1942), 553-554.
  • [4] J. Hashimoto, Direct, subdirect decompositions and congruence relations.Osaka Math. J., 9 (1957), 87-112.
  • [5] F. Maeda, Kontinuierliche Geometrien, Grundlehren der Math. Wiss., Band XCV (1958).
  • [6] F. Maeda, Direct and subdirect factorizations of lattices, J. Sci. Hiroshima Univ., Ser. A, 15 (1951), 99-102.
  • [7] T. Tanaka, Canonical subdirect factorizations of lattices, J. Sci. Hiroshima Univ., Ser. A, 16 (1952), 239-246.