On n-normal posets
Radomír Halaš; Vinayak Joshi; Vilas Kharat
Open Mathematics (2010)
- Volume: 8, Issue: 5, page 985-991
- ISSN: 2391-5455
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topRadomír Halaš, Vinayak Joshi, and Vilas Kharat. "On n-normal posets." Open Mathematics 8.5 (2010): 985-991. <http://eudml.org/doc/269334>.
@article{RadomírHalaš2010,
abstract = {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.},
author = {Radomír Halaš, Vinayak Joshi, Vilas Kharat},
journal = {Open Mathematics},
keywords = {n-normal poset; Distributive poset; Prime ideal; Unique minimal prime ideal; Polar; -normal poset; distributive poset; prime ideal; unique minimal prime ideal; polar},
language = {eng},
number = {5},
pages = {985-991},
title = {On n-normal posets},
url = {http://eudml.org/doc/269334},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Radomír Halaš
AU - Vinayak Joshi
AU - Vilas Kharat
TI - On n-normal posets
JO - Open Mathematics
PY - 2010
VL - 8
IS - 5
SP - 985
EP - 991
AB - 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.
LA - eng
KW - n-normal poset; Distributive poset; Prime ideal; Unique minimal prime ideal; Polar; -normal poset; distributive poset; prime ideal; unique minimal prime ideal; polar
UR - http://eudml.org/doc/269334
ER -
References
top- [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 Zbl0795.06006
- [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 Zbl0838.06003
- [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 Zbl1155.06002
- [7] Halaš R., Rachůnek J., Polars and prime ideals in ordered sets, Discuss. Math. Algebra Stoch. Methods, 1995, 15(1), 43–59 Zbl0840.06003
- [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 Zbl1155.06003
- [10] Lee K.B., Equational classes of distributive pseudocomplemented lattices, Canad. J. Math., 1970, 22(4), 881–891 Zbl0244.06009
- [11] Nimbhorkar S.K., Wasadikar M.P., n-normal join-semilattices, J. Indian Math. Soc. (N.S.), 2005, 72(1–4), 53–57 Zbl1121.06004
- [12] Pawar Y.S., Characterizations of normal lattices, Indian J. Pure Appl. Math., 1993, 24(11), 651–656 Zbl0801.06020
- [13] Zaanen A.C., Riesz spaces II, North-Holland Mathematical Library, 30, North-Holland, Amsterdam-New York-Oxford, 1983
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