| Title:
|
The Role of Halaš Identity in Orthomodular Lattices (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
19-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter. (English) |
| Keyword:
|
ortholattice |
| Keyword:
|
orthomodular lattice |
| Keyword:
|
antitone involution |
| Keyword:
|
principal filter |
| Keyword:
|
basic algebra |
| MSC:
|
03G25 |
| MSC:
|
06C15 |
| idZBL:
|
Zbl 06416939 |
| idMR:
|
MR3329228 |
| . |
| Date available:
|
2014-09-01T07:51:57Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143913 |
| . |
| Reference:
|
[1] Beran, L.: Orthomodular Lattices – Algebraic Approach. Academia & D. Reidel Publ. Comp, Praha & Dordrecht, 1984. MR 0785005 |
| Reference:
|
[2] Chajda, I.: Basic algebras and their applications, an overview. In: Proc. of the Salzburg Conference AAA81, Contributions to General Algebra 20, Verlag J. Heyn, Klagenfurt, 2011, 1–10. MR 2908429 |
| Reference:
|
[3] Chajda, I.: Horizontal sums of basic algebras. Discuss. Math., General Algebra Appl. 29 (2009), 21–33. Zbl 1194.06005, MR 2598600, 10.7151/dmgaa.1149 |
| Reference:
|
[4] Chajda, I., Halaš, R., Kühr, J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged) 71 (2005), 19–33. Zbl 1099.06006, MR 2160352 |
| Reference:
|
[5] Chajda, I., Halaš, R., Kühr, J.: Many-valued quantum algebras. Algebra Universalis 60 (2009), 63–90. Zbl 1219.06013, MR 2480632, 10.1007/s00012-008-2086-9 |
| Reference:
|
[6] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures. Heldermann Verlag, Lemgo, Germany, 2007. Zbl 1117.06001, MR 2326262 |
| Reference:
|
[7] Kalmbach, G.: Orthomodular Lattices. Academic Press, London–New York, 1983. Zbl 0528.06012, MR 0716496 |
| . |
