# Ideals in distributive posets

Cyndyma Batueva; Marina Semenova

Open Mathematics (2011)

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

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topCyndyma 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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