Abstract
We compute the subdirectly irreducible factors of the free Hermitean (semi)lattice generated by a single element a subject to the relation a≤a ⊥; we also compute the factors of its induced distributive presentation.
Similar content being viewed by others
References
Gross, H. (1979) Quadratic Forms in Infinite Dimensional Vector Spaces, Birkhäuser, Boston.
Gross, H. (1987) Lattices and infinite-dimensional forms. “The lattice method,” Order 4, 233–256.
Gross, H., Lomecky, Z. and Schuppli, R. (1985) Lattice problems originating in quadratic space theory, Alg. Univ. 20, 267–291.
Gross, H., Herrmann, C. and Moresi, R. (1987) The classification of subspaces in Hermitean vectorspaces, J. of Alg. 105(2), 516–541.
Herrmann, C. (1994) Galois lattices, Note di Matematica e Fisica 7, 229–234, CERFIM, Locarno.
Jónsson, B. (1955) Distributive sublattices of a modular lattice, Proc. AMS 6, 682–688.
Keller, H. A., Künzi, U. M. and Wild, M. (eds) (1998) Orthogonal Geometry in Infinite Dimensional Vector Spaces, Vol. 53. Bayreuther Mathematische Schriften, Bayreuth.
Moresi, R. (1986) Modular lattices and Hermitean forms, Alg. Univ. 22, 279–297.
Moresi, R. (1994) Hermitean (semi)lattices with indexfunction, Note di Matematica e Fisica 7, 235–242, CERFIM, Locarno.
Walter, M. (1988) Kongruenzprobleme in Unendlichdimensionalen Quadratischen Räumen, PhD-Thesis, University of Zürich.
Wille, R. (1973) On free modular lattices generated by finite chains, Alg. Univ. 3, 131–138.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Moresi, R. A Test-Example of a Quadratic Lattice. Order 17, 215–226 (2000). https://doi.org/10.1023/A:1026578524742
Issue Date:
DOI: https://doi.org/10.1023/A:1026578524742