, Volume 2, Issue 2, pp 211–213 | Cite as

Prime elements from prime ideals

  • B. Banaschewski


The prime ideal theorem for distributive lattices (PIT) is shown to imply that any complete distributive lattice with a compact unit has a prime element, which is then used to deduce from PIT that (1) every nontrivial ring with unit has a prime ideal, and (2) every Wallman locale is spatial.

AMS (MOS) subject classifications (1980)

03E25 06D99 16A66 

Key words

Prime Ideal Theorem Boolean Ultrafilter Theorem distributive lattice prime ideals in rings 


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Copyright information

© D. Reidel Publishing Company 1985

Authors and Affiliations

  • B. Banaschewski
    • 1
  1. 1.Department of Mathematical SciencesHamiltonCanada

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