English

Factoring formal power series over principal ideal domains

Commutative Algebra 2012-06-28 v4 Number Theory

Abstract

We provide an irreducibility test and factoring algorithm (with some qualifications) for formal power series in the unique factorization domain R[[X]]R[[X]], where RR is any principal ideal domain. We also classify all integral domains arising as quotient rings of R[[X]]R[[X]]. Our main tool is a generalization of the pp-adic Weierstrass preparation theorem to the context of complete filtered commutative rings.

Keywords

Cite

@article{arxiv.1107.4860,
  title  = {Factoring formal power series over principal ideal domains},
  author = {Jesse Elliott},
  journal= {arXiv preprint arXiv:1107.4860},
  year   = {2012}
}

Comments

23 pages. Final version