Variety Invariants for Modular Lattices
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 279-283
Voir la notice de l'article provenant de la source Cambridge University Press
A variety (primitive class) is a class of abstract algebras which is closed under the formation of subalgebras, homomorphic images, and products. For a given variety we shall call a function μ*, which assigns to each algebra a natural number or ∞, denoted by μ*(A), a variety invariant if for every natural number n the class of all with μ*(A) ≦ n is again a variety. In this paper, a general method of finding variety invariants for the variety of all modular lattices will be developed. This method will be based on the concept of a quotient tree of a modular lattice. As examples of variety invariants we shall define, using the general result, the primitive length and the primitive width of modular lattices.
Wille, Rudolf. Variety Invariants for Modular Lattices. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 279-283. doi: 10.4153/CJM-1969-029-2
@article{10_4153_CJM_1969_029_2,
author = {Wille, Rudolf},
title = {Variety {Invariants} for {Modular} {Lattices}},
journal = {Canadian journal of mathematics},
pages = {279--283},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-029-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-029-2/}
}
[1] 1. Cohn, P. M., Universal algebra (Harper and Row, New York-London, 1965). Google Scholar
[2] 2. Maeda, F., Kontinuierliche Geometrien (Springer-Verlag, Berlin, 1958). Google Scholar
[3] 3. Ore, O., Theory of graphs, Amer. Math. Soc. Colloq. Publ., Vol. 38 (Amer. Math. Soc, Providence, R.I., 1962). Google Scholar
Cité par Sources :