Valuations on modular lattices
Mathematica Bohemica (1991)
- Volume: 116, Issue: 4, page 391-395
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topJakubík, Ján. "Valuations on modular lattices." Mathematica Bohemica 116.4 (1991): 391-395. <http://eudml.org/doc/29175>.
@article{Jakubík1991,
abstract = {It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class $\mathcal \{K\}$ of modular lattices is defined and it is proved that each lattice belonging to $\mathcal \{K\}$ has a nontrivial valuation. Next, a result of $G$. Birkhoff concerning valuations on modular lattices of finite length is generalized.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {modular lattices; prime quotients; order-dense quotients; valuation; discrete valuation; modular lattices; prime quotients; order-dense quotients; valuation},
language = {eng},
number = {4},
pages = {391-395},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Valuations on modular lattices},
url = {http://eudml.org/doc/29175},
volume = {116},
year = {1991},
}
TY - JOUR
AU - Jakubík, Ján
TI - Valuations on modular lattices
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 4
SP - 391
EP - 395
AB - It is well-known that there exist infinite modular lattices possessing no non-trivial valuations. In this paper a class $\mathcal {K}$ of modular lattices is defined and it is proved that each lattice belonging to $\mathcal {K}$ has a nontrivial valuation. Next, a result of $G$. Birkhoff concerning valuations on modular lattices of finite length is generalized.
LA - eng
KW - modular lattices; prime quotients; order-dense quotients; valuation; discrete valuation; modular lattices; prime quotients; order-dense quotients; valuation
UR - http://eudml.org/doc/29175
ER -
References
top- G. Birkhoff, Lattice Theory, Providence 1967. (1967) Zbl0153.02501MR0227053
- G. Grätzer, General Lattice Theory, Akademie Verlag, Berlin, 1978. (1978) MR0504338
- B. Monjardet, 10.1016/0012-365X(81)90206-5, Discrete Math. 35 (1981), 173-184. (1981) Zbl0463.46016MR0620670DOI10.1016/0012-365X(81)90206-5
- E. T. Schmidt, Über die Kongruenzverbände der Verbände, Publ. Math. Debrecen 9 (1962), 245-256. (1962) Zbl0178.33902MR0151405
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.