α -ideals and annihilator ideals in 0-distributive lattices

Y. S. Pawar; S. S. Khopade

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2010)

  • Volume: 49, Issue: 1, page 63-74
  • ISSN: 0231-9721

Abstract

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In a 0-distributive lattice sufficient conditions for an α -ideal to be an annihilator ideal and prime ideal to be an α -ideal are given. Also it is proved that the images and the inverse images of α -ideals are α -ideals under annihilator preserving homomorphisms.

How to cite

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Pawar, Y. S., and Khopade, S. S.. "$\alpha $-ideals and annihilator ideals in 0-distributive lattices." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 49.1 (2010): 63-74. <http://eudml.org/doc/116478>.

@article{Pawar2010,
abstract = {In a 0-distributive lattice sufficient conditions for an $\alpha $-ideal to be an annihilator ideal and prime ideal to be an $\alpha $-ideal are given. Also it is proved that the images and the inverse images of $\alpha $-ideals are $\alpha $-ideals under annihilator preserving homomorphisms.},
author = {Pawar, Y. S., Khopade, S. S.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice; 0-distributive lattice; alpha-ideal; annihilator ideal; quasi-complemented lattice},
language = {eng},
number = {1},
pages = {63-74},
publisher = {Palacký University Olomouc},
title = {$\alpha $-ideals and annihilator ideals in 0-distributive lattices},
url = {http://eudml.org/doc/116478},
volume = {49},
year = {2010},
}

TY - JOUR
AU - Pawar, Y. S.
AU - Khopade, S. S.
TI - $\alpha $-ideals and annihilator ideals in 0-distributive lattices
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2010
PB - Palacký University Olomouc
VL - 49
IS - 1
SP - 63
EP - 74
AB - In a 0-distributive lattice sufficient conditions for an $\alpha $-ideal to be an annihilator ideal and prime ideal to be an $\alpha $-ideal are given. Also it is proved that the images and the inverse images of $\alpha $-ideals are $\alpha $-ideals under annihilator preserving homomorphisms.
LA - eng
KW - 0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice; 0-distributive lattice; alpha-ideal; annihilator ideal; quasi-complemented lattice
UR - http://eudml.org/doc/116478
ER -

References

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  1. Balasubramani, P., Venkatanarsimhan, Characterizations of the 0-distributive lattice, Indian J. Pure Appl. Math. 32, 3 (2001), 315–324. (2001) MR1826759
  2. Balasubramani, P., Stone topology of the set of the set of prime filters of a 0-distributive lattice, Indian J. Pure Appl. Math. 35, 2 (2004), 149–158. (2004) MR2040729
  3. Cornish, W. H., 10.1017/S1446788700012775, J. Aust. Math. Soc. 15, 1 (1975), 70–77. (1975) MR0344170DOI10.1017/S1446788700012775
  4. Grätzer, G., Lattice Theory – First concepts and distributive lattices, Freeman and Company, San Francisco, 1971. (1971) MR0321817
  5. Jayaram, C., Prime α -ideals in a 0-distributive lattice, Indian J. Pure Appl. Math. 17, 3 (1986), 331–337. (1986) Zbl0595.06010MR0835346
  6. Pawar, Y. S., Mane, D. N., α -ideals in 0-distributive semilattices and 0-distributive lattices, Indian J. Pure Appl. Math. 24, 7-8 (1993), 435–443. (1993) Zbl0789.06005MR1234802
  7. Varlet, J., A generalization of the notion of pseudo-complementedness, Bull. Soc. Roy. Liege 37 (1968), 149–158. (1968) Zbl0162.03501MR0228390

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