| Title:
|
Annihilator-preserving congruence relations in distributive nearlattices (English) |
| Author:
|
Calomino, Ismael |
| Author:
|
Celani, Sergio |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
143 |
| Issue:
|
4 |
| Year:
|
2018 |
| Pages:
|
391-407 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations. (English) |
| Keyword:
|
distributive nearlattice |
| Keyword:
|
ideal |
| Keyword:
|
filter |
| Keyword:
|
congruence |
| Keyword:
|
annihilator |
| MSC:
|
03G10 |
| MSC:
|
06A12 |
| MSC:
|
06D50 |
| idZBL:
|
Zbl 06997373 |
| idMR:
|
MR3895263 |
| DOI:
|
10.21136/MB.2018.0030-17 |
| . |
| Date available:
|
2018-11-29T09:24:36Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147476 |
| . |
| Reference:
|
[1] Abbott, J. C.: Semi-boolean algebra.Mat. Vesn., N. Ser. 19 (1967), 177-198. Zbl 0153.02704, MR 0239957 |
| Reference:
|
[2] Araújo, J., Kinyon, M.: Independent axiom systems for nearlattices.Czech. Math. J. 61 (2011), 975-992. Zbl 1249.06003, MR 2886250, 10.1007/s10587-011-0062-6 |
| Reference:
|
[3] Calomino, I., Celani, S.: A note on annihilators in distributive nearlattices.Miskolc Math. Notes 16 (2015), 65-78. Zbl 1340.06007, MR 3384588, 10.18514/MMN.2015.1325 |
| Reference:
|
[4] Celani, S. A.: Topological representation of distributive semilattices.Sci. Math. Jpn. 58 (2003), 55-65. Zbl 1041.06002, MR 1987817 |
| Reference:
|
[5] Celani, S. A.: Remarks on annihilators preserving congruence relations.Math. Slovaca 62 (2012), 389-398. Zbl 1312.06002, MR 2915604, 10.2478/s12175-012-0016-y |
| Reference:
|
[6] Celani, S. A.: Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices.Open Math. 13 (2015), 165-177. Zbl 1334.06005, MR 3314172, 10.1515/math-2015-0016 |
| Reference:
|
[7] Celani, S., Calomino, I.: Stone style duality for distributive nearlattices.Algebra Universalis 71 (2014), 127-153. Zbl 1301.06030, MR 3183387, 10.1007/s00012-014-0269-0 |
| Reference:
|
[8] Chajda, I., Halaš, R.: An example of a congruence distributive variety having no near-unanimity term.Acta Univ. M. Belii, Ser. Math. 13 (2006), 29-31. Zbl 1132.08002, MR 2353310 |
| Reference:
|
[9] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures.Research and Exposition in Mathematics 30. Heldermann Verlag, Lemgo (2007). Zbl 1117.06001, MR 2326262 |
| Reference:
|
[10] Chajda, I., Kolařík, M.: Ideals, congruences and annihilators on nearlattices.Acta Univ. Palacki. Olomuc., Fac. Rerum Natur. Math. 46 (2007), 25-33. Zbl 1147.06002, MR 2387490 |
| Reference:
|
[11] Chajda, I., Kolařík, M.: Nearlattices.Discrete Math. 308 (2008), 4906-4913. Zbl 1151.06004, MR 2446101, 10.1016/j.disc.2007.09.009 |
| Reference:
|
[12] Cornish, W. H.: Normal lattices.J. Aust. Math. Soc. 14 (1972), 200-215. Zbl 0247.06009, MR 0313148, 10.1017/S1446788700010041 |
| Reference:
|
[13] Cornish, W. H.: Quasicomplemented lattices.Commentat. Math. Univ. Carolinae 15 (1974), 501-511. Zbl 0293.06006, MR 0354468 |
| Reference:
|
[14] Cornish, W. H., Hickman, R. C.: Weakly distributive semilattices.Acta Math. Acad. Sci. Hung. 32 (1978), 5-16. Zbl 0497.06005, MR 0551490, 10.1007/BF01902195 |
| Reference:
|
[15] Halaš, R.: Subdirectly irreducible distributive nearlattices.Miskolc Math. Notes 7 (2006), 141-146. Zbl 1120.06003, MR 2310273, 10.18514/MMN.206.140 |
| Reference:
|
[16] Hickman, R.: Join algebras.Commun. Algebra 8 (1980), 1653-1685. Zbl 0436.06003, MR 0585925, 10.1080/00927878008822537 |
| Reference:
|
[17] Janowitz, M. F.: Annihilator preserving congruence relations of lattices.Algebra Univers. 5 (1975), 391-394. Zbl 0333.06005, MR 0392729, 10.1007/BF02485272 |
| Reference:
|
[18] Stone, M. H.: Topological representations of distributive lattices and Brouwerian logics.Čas. Mat. Fys. 67 (1937), 1-25. Zbl 0018.00303 |
| . |
