Annihilator-preserving congruence relations in distributive nearlattices

Ismael Calomino; Sergio A. Celani

Mathematica Bohemica (2018)

  • Volume: 143, Issue: 4, page 391-407
  • ISSN: 0862-7959

Abstract

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In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.

How to cite

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Calomino, Ismael, and Celani, Sergio A.. "Annihilator-preserving congruence relations in distributive nearlattices." Mathematica Bohemica 143.4 (2018): 391-407. <http://eudml.org/doc/294671>.

@article{Calomino2018,
abstract = {In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.},
author = {Calomino, Ismael, Celani, Sergio A.},
journal = {Mathematica Bohemica},
keywords = {distributive nearlattice; ideal; filter; congruence; annihilator},
language = {eng},
number = {4},
pages = {391-407},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Annihilator-preserving congruence relations in distributive nearlattices},
url = {http://eudml.org/doc/294671},
volume = {143},
year = {2018},
}

TY - JOUR
AU - Calomino, Ismael
AU - Celani, Sergio A.
TI - Annihilator-preserving congruence relations in distributive nearlattices
JO - Mathematica Bohemica
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 143
IS - 4
SP - 391
EP - 407
AB - In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.
LA - eng
KW - distributive nearlattice; ideal; filter; congruence; annihilator
UR - http://eudml.org/doc/294671
ER -

References

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  1. Abbott, J. C., Semi-boolean algebra, Mat. Vesn., N. Ser. 19 (1967), 177-198. (1967) Zbl0153.02704MR0239957
  2. Araújo, J., Kinyon, M., 10.1007/s10587-011-0062-6, Czech. Math. J. 61 (2011), 975-992. (2011) Zbl1249.06003MR2886250DOI10.1007/s10587-011-0062-6
  3. Calomino, I., Celani, S., 10.18514/MMN.2015.1325, Miskolc Math. Notes 16 (2015), 65-78. (2015) Zbl1340.06007MR3384588DOI10.18514/MMN.2015.1325
  4. Celani, S. A., Topological representation of distributive semilattices, Sci. Math. Jpn. 58 (2003), 55-65. (2003) Zbl1041.06002MR1987817
  5. Celani, S. A., 10.2478/s12175-012-0016-y, Math. Slovaca 62 (2012), 389-398. (2012) Zbl1312.06002MR2915604DOI10.2478/s12175-012-0016-y
  6. Celani, S. A., 10.1515/math-2015-0016, Open Math. 13 (2015), 165-177. (2015) Zbl1334.06005MR3314172DOI10.1515/math-2015-0016
  7. Celani, S., Calomino, I., 10.1007/s00012-014-0269-0, Algebra Universalis 71 (2014), 127-153. (2014) Zbl1301.06030MR3183387DOI10.1007/s00012-014-0269-0
  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. (2006) Zbl1132.08002MR2353310
  9. Chajda, I., Halaš, R., Kühr, J., Semilattice Structures, Research and Exposition in Mathematics 30. Heldermann Verlag, Lemgo (2007). (2007) Zbl1117.06001MR2326262
  10. Chajda, I., Kolařík, M., Ideals, congruences and annihilators on nearlattices, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur. Math. 46 (2007), 25-33. (2007) Zbl1147.06002MR2387490
  11. Chajda, I., Kolařík, M., 10.1016/j.disc.2007.09.009, Discrete Math. 308 (2008), 4906-4913. (2008) Zbl1151.06004MR2446101DOI10.1016/j.disc.2007.09.009
  12. Cornish, W. H., 10.1017/S1446788700010041, J. Aust. Math. Soc. 14 (1972), 200-215. (1972) Zbl0247.06009MR0313148DOI10.1017/S1446788700010041
  13. Cornish, W. H., Quasicomplemented lattices, Commentat. Math. Univ. Carolinae 15 (1974), 501-511. (1974) Zbl0293.06006MR0354468
  14. Cornish, W. H., Hickman, R. C., 10.1007/BF01902195, Acta Math. Acad. Sci. Hung. 32 (1978), 5-16. (1978) Zbl0497.06005MR0551490DOI10.1007/BF01902195
  15. Halaš, R., 10.18514/MMN.206.140, Miskolc Math. Notes 7 (2006), 141-146. (2006) Zbl1120.06003MR2310273DOI10.18514/MMN.206.140
  16. Hickman, R., 10.1080/00927878008822537, Commun. Algebra 8 (1980), 1653-1685. (1980) Zbl0436.06003MR0585925DOI10.1080/00927878008822537
  17. Janowitz, M. F., 10.1007/BF02485272, Algebra Univers. 5 (1975), 391-394. (1975) Zbl0333.06005MR0392729DOI10.1007/BF02485272
  18. Stone, M. H., Topological representations of distributive lattices and Brouwerian logics, Čas. Mat. Fys. 67 (1937), 1-25. (1937) Zbl0018.00303

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