// Workers AI · dad joke modeWhat did the Cohen ring say? "I'm in a bound state

Not to be confused with Cohen–Macaulay ring.

For the Boolean algebras used in set theory, see Cohen algebra.

In algebra, a Cohen ring is a field or a complete discrete valuation ring of mixed characteristic $(0,p)$ whose maximal ideal is generated by p. Cohen rings are used in the Cohen structure theorem for complete Noetherian local rings.

See also

• Norm field

References

• Cohen, I. S. (1946), "On the structure and ideal theory of complete local rings", Transactions of the American Mathematical Society, 59 (1): 54–106, doi:10.2307/1990313, ISSN 0002-9947, JSTOR 1990313, MR 0016094 Cohen's paper was written when "local ring" meant what is now called a "Noetherian local ring".
• Grothendieck, Alexandre; Dieudonné, Jean (1964). "Éléments de géométrie algébrique: IV. Étude locale des schémas et des morphismes de schémas, Première partie". Publications Mathématiques de l'IHÉS. 20: 5–259. doi:10.1007/bf02684747. MR 0173675.