Ideals in distributive posets

Cyndyma Batueva; Marina Semenova

Open Mathematics (2011)

  • Volume: 9, Issue: 6, page 1380-1388
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Cyndyma Batueva, and Marina Semenova. "Ideals in distributive posets." Open Mathematics 9.6 (2011): 1380-1388. <http://eudml.org/doc/269163>.

@article{CyndymaBatueva2011,
abstract = {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.},
author = {Cyndyma Batueva, Marina Semenova},
journal = {Open Mathematics},
keywords = {Poset; Ideal; Prime ideal; Distributive; Normal; Completion; distributive poset; prime ideal; -normal meet-semilattice; completion},
language = {eng},
number = {6},
pages = {1380-1388},
title = {Ideals in distributive posets},
url = {http://eudml.org/doc/269163},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Cyndyma Batueva
AU - Marina Semenova
TI - Ideals in distributive posets
JO - Open Mathematics
PY - 2011
VL - 9
IS - 6
SP - 1380
EP - 1388
AB - 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.
LA - eng
KW - Poset; Ideal; Prime ideal; Distributive; Normal; Completion; distributive poset; prime ideal; -normal meet-semilattice; completion
UR - http://eudml.org/doc/269163
ER -

References

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  10. [10] Halaš R., Relative polars in ordered sets, Czechoslovak Math. J., 2000, 50(125)(2), 415–429 Zbl1047.06001
  11. [11] Halaš R., Rachůnek J., Polars in ordered sets, Discuss. Math., 1995, 15(1), 43–59 Zbl0840.06003
  12. [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 Zbl1234.06003
  13. [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 Zbl1155.06003

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