| Title:
|
Sheffer operation in ortholattices (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
19-23 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We introduce the concept of Sheffer operation in ortholattices and, more generally, in lattices with antitone involution. By using this, all the fundamental operations of an ortholattice or a lattice with antitone involution are term functions built up from the Sheffer operation. We list axioms characterizing the Sheffer operation in these lattices. (English) |
| Keyword:
|
ortholattice |
| Keyword:
|
orthocomplementation |
| Keyword:
|
lattice with antitone involution |
| Keyword:
|
Sheffer operation |
| MSC:
|
06C15 |
| MSC:
|
06E30 |
| idZBL:
|
Zbl 1091.06007 |
| idMR:
|
MR2218564 |
| . |
| Date available:
|
2009-08-21T06:48:34Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133381 |
| . |
| Reference:
|
[1] Birkhoff G.: Lattice Theory. : Proc. Amer. Math. Soc., Providence, R. I., third edition, 1967. MR 0227053 |
| Reference:
|
[2] Grätzer G.: General Lattice Theory. : Birkhäuser Verlag, Basel., second edition, 1998. MR 1670580 |
| Reference:
|
[3] Sheffer H. M.: A set of five independent postulates for Boolean algebras.Trans. Amer. Math. Soc. 14 (1913), 481–488. MR 1500960 |
| . |
