Pacific Journal of Mathematics

Congruence lattices of algebras of fixed similarity type. I.

Ralph Freese, William A. Lampe, and Walter Taylor

Article information

Source
Pacific J. Math., Volume 82, Number 1 (1979), 59-68.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102785060

Mathematical Reviews number (MathSciNet)
MR549832

Zentralblatt MATH identifier
0408.06002

Subjects
Primary: 08A30: Subalgebras, congruence relations

Citation

Freese, Ralph; Lampe, William A.; Taylor, Walter. Congruence lattices of algebras of fixed similarity type. I. Pacific J. Math. 82 (1979), no. 1, 59--68. https://projecteuclid.org/euclid.pjm/1102785060


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References

  • [1] P. Crawley and R. P. Dilworth, Algebraic Theory of Lattices, Prentice-Hall, Engle- wood Cliffs, N. J., 1973.
  • [2] R. Freese, Congruence lattices of finitely generated modular lattices, Proc. Lattice Theory Conf., Ulm 1975, G. Kalmbach, Editor, 62-70.
  • [3] G. Gratzer, Universal Algebra, D. Van Nostrand Co., Inc., Princeton, N. J., 1968.
  • [4] G. Gratzer, Lattice Theory, First concepts and distributive lattices, H. M. Freeman, San Francisco, 1971.
  • [5] G. Gratzer and E. T. Schmidt, On congruences of lattices, Acta Math. Acad. Sci. Hung., 13 (1962), 179-185.
  • [6] G. Gratzer and E. T. Schmidt, Characterizations of congruence lattices of abstract algebras, Acta Sci. Math. (Szeged), 24 (1963), 34-59.
  • [7] W. Hanf, Representations of lattices of subalgebras (Preliminary report), Bull. Amer. Math. Soc, 62 (1956), 402.
  • [8] B. Jnsson, Topics in Universal Algebra, Lecture Notes in Mathematics vol. '250, Springer-Verlag, Berlin, 1972.
  • [9] B. Jnsson, Varieties of algebras and their congruence varieties, Pros. Int. Congress Math., Vancouver 1974, 315-320.
  • [10] W. A. Lampe, The independence of certain related structuresof a universal algebra I-IV, Alg. Univ., 2 (1972), 99-112, 270-283, 286-295, 296-302.
  • [11] W. A. Lampe, Notes on the congruence lattices of algebras of finite type, (1975 manu- script).
  • [12] W. A. Lampe, A note on algebras of fixed similaritytype, Abstract 77T-A120, Notices Amer. Math. Soc, 24 (1977), A-371.
  • [13] W. A. Lampe, Review of B. Jnsson [9], MR 55 (1978). #241.
  • [14] P. Pudlak, A new proof of the congruence lattice representationtheorem, Algebra Universalis, 6 (1976),269-275.
  • [15] E. T. Schmidt, KongruenzrelationenalgebraischerStrukturen,Mathematsche Forschungsberichte, VEB Deutscher Verlag Berlin, 1969, MR 47#136.
  • [16] E. T. Schmidt, Every finite distributivelattic is the congruence lattice of a modular lattice, Algebra Universalis, 4 (1974), 49-57.
  • [17] E. T. Schmidt, Congruence lattices of complemented modular lattices, Proceedings of the colloquium on universal algebra, Esztergom 1977, (to appear).
  • [18] W. Taylor, Congruence representationof modular lattices, Abstract 77T-A173, Notices Amer. Math. Soc, 24 (1977), A-420.

See also

  • II : William A. Lampe. Congruence lattices of algebras of fixed similarity type. II. Pacific Journal of Mathematics volume 103, issue 2, (1982), pp. 475-508.