| Title:
|
Relatively pseudocomplemented directoids (English) |
| Author:
|
Chajda, Ivan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
349-357 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called $p$-ideals. (English) |
| Keyword:
|
directoid |
| Keyword:
|
relative pseudocomplementation |
| Keyword:
|
filter |
| Keyword:
|
congruence distributivity |
| Keyword:
|
congruence weak regularity |
| MSC:
|
06A12 |
| MSC:
|
06D15 |
| MSC:
|
08B10 |
| idZBL:
|
Zbl 1212.06004 |
| idMR:
|
MR2573409 |
| . |
| Date available:
|
2009-09-23T21:34:22Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134908 |
| . |
| Reference:
|
[1] Chajda I.: Pseudocomplemented directoids.Comment. Math. Univ. Carolin. 49 (2008), 533--539. MR 2493936 |
| Reference:
|
[2] Chajda I., Halaš R., Kühr J.: Semilattice Structures.Heldermann Verlag, Lemgo (Germany), 2007, 228pp, ISBN 978-3-88538-230-0. MR 2326262 |
| Reference:
|
[3] Ježek J., Quackenbush R.: Directoids: algebraic model 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.: $łambda$-lattices.Math. Bohem. 122 (1997), 267--272. MR 1600648 |
| Reference:
|
[6] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets.Order 5 (1989), 407--423. MR 1010389, 10.1007/BF00353659 |
| . |
