| Title:
|
Ideals, congruences and annihilators on nearlattices (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Kolařík, Miroslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
25-33 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By a nearlattice is meant a join-semilattice having the property that every principal filter is a lattice with respect to the semilattice order. We introduce the concept of (relative) annihilator of a nearlattice and characterize some properties like distributivity, modularity or $0$-distributivity of nearlattices by means of certain properties of annihilators. (English) |
| Keyword:
|
nearlattice |
| Keyword:
|
semilattice |
| Keyword:
|
ideal |
| Keyword:
|
congruence |
| Keyword:
|
distributivity |
| Keyword:
|
modularity |
| Keyword:
|
$0$-distributivity |
| Keyword:
|
annihilator |
| MSC:
|
06A12 |
| MSC:
|
06C99 |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 1147.06002 |
| idMR:
|
MR2387490 |
| . |
| Date available:
|
2009-08-27T10:22:01Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133392 |
| . |
| Reference:
|
[1] Abbott J. C.: Semi-boolean algebra.Mat. Vestnik 4 (1967), 177–198. Zbl 0153.02704, MR 0239957 |
| Reference:
|
[2] Beazer R.: Hierarchies of distributive lattices satisfying annihilator conditions.J. London Math. Soc. 11 (1975), 216–222. Zbl 0335.06008, MR 0387141 |
| Reference:
|
[3] Chajda I., Kolařík M.: A decomposition of homomorphic images of nearlattices.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 45 (2006), 43–52. Zbl 1123.06002, MR 2321296 |
| Reference:
|
[4] Chajda I., Kolařík M.: Nearlattices.Discrete Math., to appear. Zbl 1151.06004, MR 2446101 |
| Reference:
|
[5] Cornish W. H.: The free implicative BCK-extension of a distributive nearlattice.Math. Japonica 27, 3 (1982), 279–286. Zbl 0496.03046, MR 0663155 |
| Reference:
|
[6] Cornish W. H., Noor A. S. A.: Standard elements in a nearlattice.Bull. Austral. Math. Soc. 26, 2 (1982), 185–213. Zbl 0523.06006, MR 0683652 |
| Reference:
|
[7] Davey B.: Some annihilator conditions on distributive lattices.Algebra Universalis 4 (1974), 316–322. Zbl 0299.06007, MR 0357261 |
| Reference:
|
[8] Davey B., Nieminen J.: Annihilators in modular lattices.Algebra Universalis 22 (1986), 154–158. Zbl 0613.06004, MR 0870463 |
| Reference:
|
[9] Grätzer G.: General Lattice Theory. : Birkhäuser Verlag., Basel, 1978. MR 0504338 |
| Reference:
|
[10] Halaš R.: Subdirectly irreducible distributive nearlattices.Math. Notes 7, 2 (2006), 141–146. Zbl 1120.06003, MR 2310273 |
| Reference:
|
[11] Hickman R.: Join algebras.Communications in Algebra 8 (1980), 1653–1685. Zbl 0436.06003, MR 0585925 |
| Reference:
|
[12] Mandelker M.: Relative annihilators in lattices.Duke Math. J. 40 (1970), 377–386. Zbl 0206.29701, MR 0256951 |
| Reference:
|
[13] Nieminen J.: The Jordan–Hölder chain condition and annihilators in finite lattices.Tsukuba J. Math. 14 (1990), 405–411. Zbl 0721.06008, MR 1085207 |
| Reference:
|
[14] Noor A. S. A., Cornish W. H.: Multipliers on a nearlattices.Commentationes Mathematicae Universitatis Carolinae (1986), 815–827. MR 0874675 |
| Reference:
|
[15] Scholander M.: Trees, lattices, order and betweenness.Proc. Amer. Math. Soc. 3 (1952), 369–381. MR 0048405 |
| Reference:
|
[16] Scholander M.: Medians and betweenness.Proc. Amer. Math. Soc. 5 (1954), 801–807. MR 0064749 |
| Reference:
|
[17] Scholander M.: Medians, lattices and trees.Proc. Amer. Math. Soc. 5 (1954), 808–812. MR 0064750 |
| . |
