On n-normal posets
Radomír Halaš ; Vinayak Joshi ; Vilas Kharat
Open Mathematics, Tome 8 (2010), p. 985-991 / Harvested from The Polish Digital Mathematics Library

A poset Q is called n-normal, if its every prime ideal contains at most n minimal prime ideals. In this paper, using the prime ideal theorem for finite ideal distributive posets, some properties and characterizations of n-normal posets are obtained.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:269334
@article{bwmeta1.element.doi-10_2478_s11533-010-0062-z,
     author = {Radom\'\i r Hala\v s and Vinayak Joshi and Vilas Kharat},
     title = {On n-normal posets},
     journal = {Open Mathematics},
     volume = {8},
     year = {2010},
     pages = {985-991},
     zbl = {1234.06003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0062-z}
}
Radomír Halaš; Vinayak Joshi; Vilas Kharat. On n-normal posets. Open Mathematics, Tome 8 (2010) pp. 985-991. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0062-z/

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

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

[3] Erné M., Distributive laws for concept lattices, Algebra Universalis, 1993, 30(4), 538–580 http://dx.doi.org/10.1007/BF01195382 | Zbl 0795.06006

[4] Grätzer G., Schmidt E.T., On a problem of M.H. Stone, Acta Math. Acad. Sci. Hung., 1957, 8(3–4), 455–460 http://dx.doi.org/10.1007/BF02020328

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

[6] Halaš R., On extensions of ideals in posets, Discrete Math., 2008, 308(21), 4972–4977 http://dx.doi.org/10.1016/j.disc.2007.09.022 | Zbl 1155.06002

[7] Halaš R., Rachůnek J., Polars and prime ideals in ordered sets, Discuss. Math. Algebra Stoch. Methods, 1995, 15(1), 43–59 | Zbl 0840.06003

[8] Johnstone P.T., Stone Spaces, Cambridge Stud. Adv. Math., 3, Cambridge University Press, Cambridge, 1982

[9] 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

[10] Lee K.B., Equational classes of distributive pseudocomplemented lattices, Canad. J. Math., 1970, 22(4), 881–891 | Zbl 0244.06009

[11] Nimbhorkar S.K., Wasadikar M.P., n-normal join-semilattices, J. Indian Math. Soc. (N.S.), 2005, 72(1–4), 53–57 | Zbl 1121.06004

[12] Pawar Y.S., Characterizations of normal lattices, Indian J. Pure Appl. Math., 1993, 24(11), 651–656 | Zbl 0801.06020

[13] Zaanen A.C., Riesz spaces II, North-Holland Mathematical Library, 30, North-Holland, Amsterdam-New York-Oxford, 1983