KommAlg Tutorium (2026)

The proofs are written for the general case of the jacobson radical (using Nakayama's Lemma for jacobson radicals). The proofs also work for local rings and maximal ideals (and using nakayama's lemma for local rings).

• surjection modulo jacobson radical for a finitely generated module
  
• injection modulo jacobson radical is in general not an injection before
  

• field not finitely generated over a proper subring
  

• functor from Proj(R) to Proj(R/J) is a conservative functor for an ideal of the jacobson radical
  

• derived hom(-,Z) is conservative
  
• here \(\mathrm{Ext}^1(-,-)\) denotes the respective quotients.