Misplaced Pages

Cohen ring

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.

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.

This commutative algebra-related article is a stub. You can help Misplaced Pages by expanding it.

v
t
e

Cohen ring Add topic