For lattices of finite length there are many characterizations of semimodularity (see, for instance, Grätzer [3] and Stern [6]–[8]). The present paper deals with some conditions characterizing semimodularity in lower continuous strongly dually atomic lattices. We give here a generalization of results of paper [7].
@article{107571,
author = {Andrzej Walendziak},
title = {Semimodularity in lower continuous strongly dually atomic lattices},
journal = {Archivum Mathematicum},
volume = {032},
year = {1996},
pages = {163-165},
zbl = {0902.06011},
mrnumber = {1421853},
language = {en},
url = {http://dml.mathdoc.fr/item/107571}
}
Walendziak, Andrzej. Semimodularity in lower continuous strongly dually atomic lattices. Archivum Mathematicum, Tome 032 (1996) pp. 163-165. http://gdmltest.u-ga.fr/item/107571/
Lattice Theory, 3rd edition, American Mathematical Society, Providence, RI, 1967. | MR 0227053 | Zbl 0537.06001
Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs (N.J.), 1973.
General Lattice Theory, Birhäuser Basel, 1978. | MR 0509213
The Kuroš-Ore Theorem, finite and infinite decompositions, Studia Sci. Math. Hungar., 17(1982), 243-250. | MR 0761540
Exchange properties in lattices of finite length, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 31 (1982), 15-26. | MR 0693283 | Zbl 0548.06003
Semimodularity in lattices of finite length, Discrete Math. 41 (1982), 287-293. | MR 0676890 | Zbl 0655.06006
Characterizations of semimodularity, Studia Sci. Math. Hungar. 25 (1990), 93-96. | MR 1102200 | Zbl 0629.06007
Semimodular Lattices, B. G. Teubner Verlagsgesellschaft, Stuttgart-Leipzig, 1991. | MR 1164868 | Zbl 0957.06008