| Title:
|
Directoids with sectionally switching involutions (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
35-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities. (English) |
| Keyword:
|
Directoid |
| Keyword:
|
commutative directoid |
| Keyword:
|
semilattice |
| Keyword:
|
involution |
| Keyword:
|
implication algebra |
| Keyword:
|
sectionally switching mapping |
| MSC:
|
03G25 |
| MSC:
|
06A11 |
| MSC:
|
06A12 |
| idZBL:
|
Zbl 1123.06001 |
| idMR:
|
MR2321295 |
| . |
| Date available:
|
2009-08-21T07:04:53Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133444 |
| . |
| Reference:
|
[1] Abbott J. C.: Semi-boolean algebras.Matem. Vestnik 4 (1967), 177–198. MR 0239957 |
| Reference:
|
[2] Chajda I.: Lattices and semilattices having an antitone involution in every upper interval.Comment. Math. Univ. Carol. 44 (2003), 577–585. Zbl 1101.06003, MR 2062874 |
| Reference:
|
[3] 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:
|
[4] Ježek J., Quackenbush R.: Directoids: algebraic models of up-directed sets., Algebra Universalis 27 (1990), 49–69. MR 1025835 |
| . |
