| Title:
|
Pseudocomplemented directoids (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
533-539 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Directoids as a generalization of semilattices were introduced by J. Je\v{z}ek and R. Quackenbush in 1990. We modify the concept of a pseudocomplement for commutative directoids and study several basic properties: the Glivenko equivalence, the set of the so-called boolean elements and an axiomatization of these algebras. (English) |
| Keyword:
|
commutative directoid |
| Keyword:
|
$\lambda$-lattice |
| Keyword:
|
pseudocomplement |
| Keyword:
|
boolean elements |
| MSC:
|
06A12 |
| MSC:
|
06A99 |
| MSC:
|
06C15 |
| MSC:
|
06D15 |
| idZBL:
|
Zbl 1212.06005 |
| idMR:
|
MR2493936 |
| . |
| Date available:
|
2009-05-05T17:13:01Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119744 |
| . |
| Reference:
|
[1] Chajda I., Halaš R., Kühr J.: Semilattice Structures.Heldermann Verlag, Lemgo (Germany), 2007, ISBN 978-3-88538-230-0. MR 2326262 |
| Reference:
|
[2] Frink O.: Pseudo-complemented semi-lattices.Duke Math. J. 29 (1962), 505-514. MR 0140449 |
| Reference:
|
[3] Ježek J., Quackenbush R.: Directoids: algebraic models of up-directed sets.Algebra Universalis 27 (1990), 49-69. MR 1025835, 10.1007/BF01190253 |
| Reference:
|
[4] Jones G.T.: Pseudo-complemented semi-lattices.Ph.D. Thesis, Univ. of California, Los Angeles, 1972. |
| Reference:
|
[5] Snášel V.: $\lambda$-lattices.Math. Bohem. 122 (1997), 267-272. MR 1600648 |
| . |
