Ideals in distributive posets
Cyndyma Batueva ; Marina Semenova
Open Mathematics, Tome 9 (2011), p. 1380-1388 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We prove that any ideal in a distributive (relative to a certain completion) poset is an intersection of prime ideals. Besides that, we give a characterization of n-normal meet semilattices with zero, thus generalizing a known result for lattices with zero.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:269163 
@article{bwmeta1.element.doi-10_2478_s11533-011-0075-2,
     author = {Cyndyma Batueva and Marina Semenova},
     title = {Ideals in distributive posets},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {1380-1388},
     zbl = {1242.06002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0075-2}
}

Cyndyma Batueva; Marina Semenova. Ideals in distributive posets. Open Mathematics, Tome 9 (2011) pp. 1380-1388. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0075-2/

[1] Birkhoff G., Lattice Theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, Providence, 1967

[2] Chajda I., Halaš R., Indexed annihilators in ordered sets, Math. Slovaca, 1995, 45(5), 501–508 | Zbl 0843.06002

[3] Cornish W.H., Normal lattices, J. Aust. Math. Soc., 1972, 14(2), 200–215 http://dx.doi.org/10.1017/S1446788700010041

[4] Cornish W.H., n-normal lattices, Proc. Amer. Math. Soc., 1974, 45(1), 48–54

[5] Grätzer G., General Lattice Theory, 2nd ed., Birkhäuser, Basel, 1998

[6] Halaš R., Characterization of distributive sets by generalized annihilators, Arch. Math. (Brno), 1994, 30(1), 25–27 | Zbl 0805.06001

[7] Halaš R., Decomposition of directed sets with zero, Math. Slovaca, 1995, 45(1), 9–17 | Zbl 0833.06001

[8] Halaš R., Annihilators and ideals in ordered sets, Czechoslovak Math. J., 1995, 45(120)(1), 127–134 | Zbl 0838.06003

[9] Halaš R., Boolean algebra of polars as a reflector, In: Contributions to General Algebra, 10, Heyn, Klagenfurt, 1998, 177–187 | Zbl 0904.06003

[10] Halaš R., Relative polars in ordered sets, Czechoslovak Math. J., 2000, 50(125)(2), 415–429 | Zbl 1047.06001

[11] Halaš R., Rachůnek J., Polars in ordered sets, Discuss. Math., 1995, 15(1), 43–59 | Zbl 0840.06003

[12] Halaš R., Joshi V., Kharat V.S., On n-normal posets, Cent. Eur. J. Math., 2010, 8(5), 985–991 http://dx.doi.org/10.2478/s11533-010-0062-z | Zbl 1234.06003

[13] Kharat V.S., Mokbel K.A., Semiprime ideals and separation theorems for posets, Order, 2008, 25(3), 195–210 http://dx.doi.org/10.1007/s11083-008-9087-3 | Zbl 1155.06003