Krull's separation lemma

In abstract algebra, Krull's separation lemma is a lemma in ring theory. It was proved by Wolfgang Krull in 1928.[1]

Statement of the lemma

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Let   be an ideal and let   be a multiplicative system (i.e.   is closed under multiplication) in a ring  , and suppose  . Then there exists a prime ideal   satisfying   and  .[2]

References

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  1. ^ Krull, Wolfgang (1928). "Zur Theorie der zweiseitigen Ideale in nichtkommutativen Bereichen". Mathematische Zeitschrift. 28 (1): 481–503. doi:10.1007/BF01181179. ISSN 0025-5874. S2CID 122870138.
  2. ^ Sun, Shu-Hao (1992). "On separation lemmas". Journal of Pure and Applied Algebra. 78 (3): 301–310. doi:10.1016/0022-4049(92)90112-S.