Geodesic
$\alpha $-ideals and annihilator ideals in 0-distributive lattices
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 63-74 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06D99
Keywords: 0-distributive lattice; $\alpha $-ideal; annihilator ideal; quasi-complemented lattice 
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Pawar, Y. S.; Khopade, S. S. $\alpha $-ideals and annihilator ideals in 0-distributive lattices. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 49 (2010) no. 1, pp. 63-74. http://geodesic.mathdoc.fr/item/AUPO_2010_49_1_a6/

[1] Balasubramani, P., Venkatanarsimhan: Characterizations of the 0-distributive lattice. Indian J. Pure Appl. Math. 32, 3 (2001), 315–324. | MR

[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. | MR

[3] Cornish, W. H.: Annulets and $\propto $-ideals in a distributive lattice. J. Aust. Math. Soc. 15, 1 (1975), 70–77. | DOI | MR

[4] Grätzer, G.: Lattice Theory – First concepts and distributive lattices. Freeman and Company, San Francisco, 1971. | MR

[5] Jayaram, C.: Prime $\alpha $-ideals in a 0-distributive lattice. Indian J. Pure Appl. Math. 17, 3 (1986), 331–337. | MR | Zbl

[6] Pawar, Y. S., Mane, D. N.: $\alpha $-ideals in 0-distributive semilattices and 0-distributive lattices. Indian J. Pure Appl. Math. 24, 7-8 (1993), 435–443. | MR | Zbl

[7] Varlet, J.: A generalization of the notion of pseudo-complementedness. Bull. Soc. Roy. Liege 37 (1968), 149–158. | MR | Zbl