Krull's separation lemma explained

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

Let

I be an ideal and let M be a multiplicative system (i.e. M is closed under multiplication) in a ring R , and suppose I \cap M = \varnothing . Then there exists a prime ideal P satisfying I \subseteq P and P \cap M = \varnothing .^[2]

References

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