# Article

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Keywords:
0-distributive lattice; $\alpha$-ideal; annihilator ideal; quasi-complemented lattice
Summary:
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.
References:
[1] Balasubramani, P., Venkatanarsimhan: Characterizations of the 0-distributive lattice. Indian J. Pure Appl. Math. 32, 3 (2001), 315–324. MR 1826759
[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 2040729
[3] Cornish, W. H.: Annulets and $\propto$-ideals in a distributive lattice. J. Aust. Math. Soc. 15, 1 (1975), 70–77. DOI 10.1017/S1446788700012775 | MR 0344170
[4] Grätzer, G.: Lattice Theory – First concepts and distributive lattices. Freeman and Company, San Francisco, 1971. MR 0321817
[5] Jayaram, C.: Prime $\alpha$-ideals in a 0-distributive lattice. Indian J. Pure Appl. Math. 17, 3 (1986), 331–337. MR 0835346 | Zbl 0595.06010
[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 1234802 | Zbl 0789.06005
[7] Varlet, J.: A generalization of the notion of pseudo-complementedness. Bull. Soc. Roy. Liege 37 (1968), 149–158. MR 0228390 | Zbl 0162.03501

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