| Title:
|
Note on $\alpha $-filters in distributive nearlattices (English) |
| Author:
|
Calomino, Ismael |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
144 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
241-250 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this short paper we introduce the notion of $\alpha $-filter in the class of distributive nearlattices and we prove that the $\alpha $-filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators. (English) |
| Keyword:
|
distributive nearlattice |
| Keyword:
|
annihilator |
| Keyword:
|
$\alpha $-filter |
| MSC:
|
03G10 |
| MSC:
|
06A12 |
| MSC:
|
06D50 |
| idZBL:
|
Zbl 07088849 |
| idMR:
|
MR3985855 |
| DOI:
|
10.21136/MB.2018.0101-17 |
| . |
| Date available:
|
2019-07-24T11:10:23Z |
| Last updated:
|
2020-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147772 |
| . |
| Reference:
|
[1] Abbott, J. C.: Semi-boolean algebra.Mat. Vesn., N. Ser. 4 (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.: $\alpha$-ideals and $\alpha$-deductive systems in bounded Hilbert algebras.J. Mult.-{}Valued Logic and Soft Computing 21 (2013), 493-510. Zbl 06930415, MR 3242515 |
| Reference:
|
[5] Celani, S.: Notes on bounded Hilbert algebras with supremum.Acta Sci. Math. 80 (2014), 3-19. Zbl 1340.05137, MR 3236248, 10.14232/actasm-012-267-9 |
| Reference:
|
[6] Celani, S., Calomino, I.: Stone style duality for distributive nearlattices.Algebra Univers. 71 (2014), 127-153. Zbl 1301.06030, MR 3183387, 10.1007/s00012-014-0269-0 |
| Reference:
|
[7] Celani, S., Calomino, I.: On homomorphic images and the free distributive lattice extension of a distributive nearlattice.Rep. Math. Logic 51 (2016), 57-73. Zbl 06700646, MR 3562693, 10.4467/20842589RM.16.001.5282 |
| 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, 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 Nat., 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.: Annulets and $\alpha$-ideals in distributive lattices.J. Aust. Math. Soc. 15 (1973), 70-77. Zbl 0274.06008, MR 0344170, 10.1017/S1446788700012775 |
| 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] González, L. J.: The logic of distributive nearlattices.Soft Computing 22 (2018), 2797-2807. 10.1007/s00500-017-2750-0 |
| Reference:
|
[16] Hickman, R.: Join algebras.Commun. Algebra 8 (1980), 1653-1685. Zbl 0436.06003, MR 0585925, 10.1080/00927878008822537 |
| . |
