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Keywords:
bounded distributive semilattice; quasicomplement; relative annihilator; order-ideal; filter
bounded distributive semilattice; quasicomplement; relative annihilator; order-ideal; filter
Summary:
We introduce some particular classes of filters and order-ideals in distributive semilattices, called $\alpha$-filters and $\alpha$-order-ideals, respectively. In particular, we study $\alpha$-filters and $\alpha$-order-ideals in distributive quasicomplemented semilattices. We also characterize the filters-congruence-cokernels in distributive quasicomplemented semilattices through $\alpha$-order-ideals.
References:
[1] Balbes R., Dwinger P.: Distributive Lattices. University of Missouri Press, Columbia, 1974. MR 0373985 | Zbl 0321.06012
[2] Celani S. A.: Topological representation of distributive semilattices. Sci. Math. Jpn. 58 (2003), no. 1, 55–65. MR 1987817 | Zbl 1041.06002
[3] Celani S. A.: Distributive pseudocomplemented semilattices. Asian-Eur. J. Math. 3 (2010), no. 1, 21–30. DOI 10.1142/S1793557110000039 | MR 2654807
[4] Celani S. A.: Remarks on annihilators preserving congruence relations. Math. Slovaca 62 (2012), no. 3, 389–398. DOI 10.2478/s12175-012-0016-y | MR 2915604
[5] Celani S. A.: Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices. Open Math. 13 (2015), no. 1, 165–177. MR 3314172
[6] Celani S., Calomino I.: Some remarks on distributive semilattices. Comment. Math. Univ. Carolin. 54 (2013), no. 3, 407–428. MR 3090419
[7] Chajda I., Halaš R., Kühr J.: Semilattice Structures. Research and Exposition in Mathematics, 30, Heldermann Verlag, Lemgo, 2007. MR 2326262
[8] Cornish W. H.: Normal lattices. J. Austral. Math. Soc. 14 (1972), 200–215. DOI 10.1017/S1446788700010041 | MR 0313148
[9] Cornish W. H.: Annulets and $\alpha$-ideals in a distributive lattice. J. Austral. Math. Soc. 15 (1973), 70–77. DOI 10.1017/S1446788700012775 | MR 0344170
[10] Cornish W.: Quasicomplemented lattices. Comment. Math. Univ. Carolinae 15 (1974), 501–511. MR 0354468
[11] Grätzer G.: General Lattice Theory. Birkhäuser Verlag, Basel, 1998. MR 1670580
[12] Jayaram C.: Quasicomplemented semilattices. Acta Math. Acad. Sci. Hungar. 39 (1982), no. 1–3, 39–47. DOI 10.1007/BF01895211 | MR 0653670
[13] Mandelker M.: Relative annihilators in lattices. Duke Math. J. 37 (1970), 377–386. DOI 10.1215/S0012-7094-70-03748-8 | MR 0256951 | Zbl 0206.29701
[14] Mokbel K. A.: $\alpha$-ideals in $0$-distributive posets. Math. Bohem. 140 (2015), no. 3, 319–328. DOI 10.21136/MB.2015.144398 | MR 3397260
[15] Murty P. V. R., Murty M. K.: Some remarks on certain classes of semilattices. Internat. J. Math. Math. Sci. 5 (1982), no. 1, 21–30. DOI 10.1155/S0161171282000039 | MR 0666490
[16] Pawar Y., Mane D.: $\alpha$-ideals in $0$-distributive semilattices and $0$-distributive lattices. Indian J. Pure Appl. Math. 24 (1993), 435–443. MR 1234802
[17] Pawar Y. S., Khopade S. S.: $\alpha$-ideals and annihilator ideals in $0$-distributive lattices. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 49 (2010), no. 1, 63–74. MR 2797524
[18] Ramana Murty P. V., Ramam V.: On filters and filter congruences in semilattices. Algebra Universalis 12 (1981), no. 3, 343–351. DOI 10.1007/BF02483894 | MR 0624300
[19] Speed T. P.: Some remarks on a class of distributive lattices. J. Austral. Math. Soc. 9 (1969), 289–296. DOI 10.1017/S1446788700007205 | MR 0246800
[20] Varlet J. C.: A generalization of the notion of pseudo-complementedness. Bull. Soc. Roy. Sci. Liège 37 (1968), 149–158. MR 0228390 | Zbl 0162.03501
[21] Varlet J. C.: Relative annihilators in semilattices. Bull. Austral. Math. Soc. 9 (1973), 169–185. DOI 10.1017/S0004972700043094 | MR 0382091 | Zbl 0258.06009
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