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Keywords:
distributive nearlattice; annihilator; $\alpha $-filter
distributive nearlattice; annihilator; $\alpha $-filter
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.
References:
[1] Abbott, J. C.: Semi-boolean algebra. Mat. Vesn., N. Ser. 4 (1967), 177-198. MR 0239957 | Zbl 0153.02704
[2] Araújo, J., Kinyon, M.: Independent axiom systems for nearlattices. Czech. Math. J. 61 (2011), 975-992. DOI 10.1007/s10587-011-0062-6 | MR 2886250 | Zbl 1249.06003
[3] Calomino, I., Celani, S.: A note on annihilators in distributive nearlattices. Miskolc Math. Notes 16 (2015), 65-78. DOI 10.18514/MMN.2015.1325 | MR 3384588 | Zbl 1340.06007
[4] Celani, S.: $\alpha$-ideals and $\alpha$-deductive systems in bounded Hilbert algebras. J. Mult.-{}Valued Logic and Soft Computing 21 (2013), 493-510. MR 3242515 | Zbl 06930415
[5] Celani, S.: Notes on bounded Hilbert algebras with supremum. Acta Sci. Math. 80 (2014), 3-19. DOI 10.14232/actasm-012-267-9 | MR 3236248 | Zbl 1340.05137
[6] Celani, S., Calomino, I.: Stone style duality for distributive nearlattices. Algebra Univers. 71 (2014), 127-153. DOI 10.1007/s00012-014-0269-0 | MR 3183387 | Zbl 1301.06030
[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. DOI 10.4467/20842589RM.16.001.5282 | MR 3562693 | Zbl 06700646
[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. MR 2353310 | Zbl 1132.08002
[9] Chajda, I., Halaš, R., Kühr, J.: Semilattice Structures. Research and Exposition in Mathematics 30. Heldermann, Lemgo (2007). MR 2326262 | Zbl 1117.06001
[10] Chajda, I., Kolařík, M.: Ideals, congruences and annihilators on nearlattices. Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 46 (2007), 25-33. MR 2387490 | Zbl 1147.06002
[11] Chajda, I., Kolařík, M.: Nearlattices. Discrete Math. 308 (2008), 4906-4913. DOI 10.1016/j.disc.2007.09.009 | MR 2446101 | Zbl 1151.06004
[12] Cornish, W. H.: Normal lattices. J. Aust. Math. Soc. 14 (1972), 200-215. DOI 10.1017/S1446788700010041 | MR 0313148 | Zbl 0247.06009
[13] Cornish, W. H.: Annulets and $\alpha$-ideals in distributive lattices. J. Aust. Math. Soc. 15 (1973), 70-77. DOI 10.1017/S1446788700012775 | MR 0344170 | Zbl 0274.06008
[14] Cornish, W. H., Hickman, R. C.: Weakly distributive semilattices. Acta Math. Acad. Sci. Hung. 32 (1978), 5-16. DOI 10.1007/BF01902195 | MR 0551490 | Zbl 0497.06005
[15] González, L. J.: The logic of distributive nearlattices. Soft Computing 22 (2018), 2797-2807. DOI 10.1007/s00500-017-2750-0
[16] Hickman, R.: Join algebras. Commun. Algebra 8 (1980), 1653-1685. DOI 10.1080/00927878008822537 | MR 0585925 | Zbl 0436.06003
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