English

On solutions for derivations of a Noetherian k-algebra and local simplicity

Commutative Algebra 2013-09-23 v1

Abstract

We introduce a general notion of solution for a Noetherian differential kk-algebra and study its relationship with simplicity, where k is an algebraically closed field; then we analyze conditions under which such solutions may exist and be unique, with special emphasis in the cases of k-algebras of finite type and formal series rings over k. Using that notion we generalize a criterion for simplicity due to Brumatti-Lequain-Levcovitz and give a geometric characterization of that; as an application we give a new proof of a classification theorem for local simplicity due to Hart and obtain a general result for simplicity of formal series rings over k

Keywords

Cite

@article{arxiv.1309.5282,
  title  = {On solutions for derivations of a Noetherian k-algebra and local simplicity},
  author = {Rene Baltazar and Ivan Pan},
  journal= {arXiv preprint arXiv:1309.5282},
  year   = {2013}
}