Ideals in distributive posets

Cyndyma Batueva 1  and Marina Semenova
  • 1 Novosibirsk State University
  • 2 Siberian Branch RAS


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.

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