Note on α -filters in distributive nearlattices

Ismael Calomino

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 3, page 241-250
  • ISSN: 0862-7959

Abstract

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In this short paper we introduce the notion of α -filter in the class of distributive nearlattices and we prove that the α -filters of a normal distributive nearlattice are strongly connected with the filters of the distributive nearlattice of the annihilators.

How to cite

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Calomino, Ismael. "Note on $\alpha $-filters in distributive nearlattices." Mathematica Bohemica 144.3 (2019): 241-250. <http://eudml.org/doc/294411>.

@article{Calomino2019,
abstract = {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.},
author = {Calomino, Ismael},
journal = {Mathematica Bohemica},
keywords = {distributive nearlattice; annihilator; $\alpha $-filter},
language = {eng},
number = {3},
pages = {241-250},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Note on $\alpha $-filters in distributive nearlattices},
url = {http://eudml.org/doc/294411},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Calomino, Ismael
TI - Note on $\alpha $-filters in distributive nearlattices
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 3
SP - 241
EP - 250
AB - 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.
LA - eng
KW - distributive nearlattice; annihilator; $\alpha $-filter
UR - http://eudml.org/doc/294411
ER -

References

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  1. Abbott, J. C., Semi-boolean algebra, Mat. Vesn., N. Ser. 4 (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., α -ideals and α -deductive systems in bounded Hilbert algebras, J. Mult.-{}Valued Logic and Soft Computing 21 (2013), 493-510. (2013) Zbl06930415MR3242515
  5. Celani, S., 10.14232/actasm-012-267-9, Acta Sci. Math. 80 (2014), 3-19. (2014) Zbl1340.05137MR3236248DOI10.14232/actasm-012-267-9
  6. Celani, S., Calomino, I., 10.1007/s00012-014-0269-0, Algebra Univers. 71 (2014), 127-153. (2014) Zbl1301.06030MR3183387DOI10.1007/s00012-014-0269-0
  7. Celani, S., Calomino, I., 10.4467/20842589RM.16.001.5282, Rep. Math. Logic 51 (2016), 57-73. (2016) Zbl06700646MR3562693DOI10.4467/20842589RM.16.001.5282
  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, Lemgo (2007). (2007) Zbl1117.06001MR2326262
  10. Chajda, I., Kolařík, M., Ideals, congruences and annihilators on nearlattices, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., 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., 10.1017/S1446788700012775, J. Aust. Math. Soc. 15 (1973), 70-77. (1973) Zbl0274.06008MR0344170DOI10.1017/S1446788700012775
  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. González, L. J., 10.1007/s00500-017-2750-0, Soft Computing 22 (2018), 2797-2807. (2018) DOI10.1007/s00500-017-2750-0
  16. Hickman, R., 10.1080/00927878008822537, Commun. Algebra 8 (1980), 1653-1685. (1980) Zbl0436.06003MR0585925DOI10.1080/00927878008822537

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