| Title:
|
Semimodularity in lower continuous strongly dually atomic lattices (English) |
| Author:
|
Walendziak, Andrzej |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
163-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
lower continuous lattices |
| Keyword:
|
strongly dually atomic lattices |
| Keyword:
|
semimodular and atomic lattices |
| MSC:
|
06B35 |
| MSC:
|
06C10 |
| idZBL:
|
Zbl 0902.06011 |
| idMR:
|
MR1421853 |
| . |
| Date available:
|
2008-06-06T21:30:44Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107571 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice Theory.3rd edition, American Mathematical Society, Providence, RI, 1967. Zbl 0537.06001, MR 0227053 |
| Reference:
|
[2] Crawley, P., Dilworth, R. P.: Algebraic Theory of Lattices.Prentice-Hall, Englewood Cliffs (N.J.), 1973. |
| Reference:
|
[3] Grätzer, G.: General Lattice Theory.Birhäuser Basel, 1978. MR 0509213 |
| Reference:
|
[4] Richter, G.: The Kuroš-Ore Theorem, finite and infinite decompositions.Studia Sci. Math. Hungar., 17(1982), 243-250. MR 0761540 |
| Reference:
|
[5] Stern, M.: Exchange properties in lattices of finite length.Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 31 (1982), 15-26. Zbl 0548.06003, MR 0693283 |
| Reference:
|
[6] Stern, M.: Semimodularity in lattices of finite length.Discrete Math. 41 (1982), 287-293. Zbl 0655.06006, MR 0676890 |
| Reference:
|
[7] Stern, M.: Characterizations of semimodularity.Studia Sci. Math. Hungar. 25 (1990), 93-96. Zbl 0629.06007, MR 1102200 |
| Reference:
|
[8] Stern, M.: Semimodular Lattices.B. G. Teubner Verlagsgesellschaft, Stuttgart-Leipzig, 1991. Zbl 0957.06008, MR 1164868 |
| . |
