Previous |  Up |  Next

Article

Keywords:
distributive nearlattice; ideal; filter; congruence; annihilator
Summary:
In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.
References:
[1] Abbott, J. C.: Semi-boolean algebra. Mat. Vesn., N. Ser. 19 (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. A.: Topological representation of distributive semilattices. Sci. Math. Jpn. 58 (2003), 55-65. MR 1987817 | Zbl 1041.06002
[5] Celani, S. A.: Remarks on annihilators preserving congruence relations. Math. Slovaca 62 (2012), 389-398. DOI 10.2478/s12175-012-0016-y | MR 2915604 | Zbl 1312.06002
[6] Celani, S. A.: Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices. Open Math. 13 (2015), 165-177. DOI 10.1515/math-2015-0016 | MR 3314172 | Zbl 1334.06005
[7] Celani, S., Calomino, I.: Stone style duality for distributive nearlattices. Algebra Universalis 71 (2014), 127-153. DOI 10.1007/s00012-014-0269-0 | MR 3183387 | Zbl 1301.06030
[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 Verlag, Lemgo (2007). MR 2326262 | Zbl 1117.06001
[10] Chajda, I., Kolařík, M.: Ideals, congruences and annihilators on nearlattices. Acta Univ. Palacki. Olomuc., Fac. Rerum Natur. 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.: Quasicomplemented lattices. Commentat. Math. Univ. Carolinae 15 (1974), 501-511. MR 0354468 | Zbl 0293.06006
[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] Halaš, R.: Subdirectly irreducible distributive nearlattices. Miskolc Math. Notes 7 (2006), 141-146. DOI 10.18514/MMN.206.140 | MR 2310273 | Zbl 1120.06003
[16] Hickman, R.: Join algebras. Commun. Algebra 8 (1980), 1653-1685. DOI 10.1080/00927878008822537 | MR 0585925 | Zbl 0436.06003
[17] Janowitz, M. F.: Annihilator preserving congruence relations of lattices. Algebra Univers. 5 (1975), 391-394. DOI 10.1007/BF02485272 | MR 0392729 | Zbl 0333.06005
[18] Stone, M. H.: Topological representations of distributive lattices and Brouwerian logics. Čas. Mat. Fys. 67 (1937), 1-25. Zbl 0018.00303
Partner of
EuDML logo