@misc{RING_5.MIZ,
      AUTHOR = {Schwarzweller, Christoph},
      TITLE = {On Roots of Polynomials and Algebraically Closed Fields},
      ADDRESS1 = {Institute of Informatics, University of Gdansk, Poland},
      SECTION1 = {Preliminaries},
      SECTION2 = {Some More Properties of Polynomials},
      SECTION3 = {On Roots of Polynomials},
      SECTION4 = {More about Bags},
      SECTION5 = {On Multiple Roots of Polynomials},
      SECTION6 = {The Polynomial $X^n + 1$},
      SECTION7 = {The polynomials $(x-a_1) * (x-a2) * \ldots * (x-a_n)$},
      SECTION8 = {Main Theorems}
      DAY = {30},
      MONTH = {August},
      YEAR = {2017},
      SUMMARY = {In this article we further extend the algebraic theory of polynomial
                 rings in Mizar \cite{Mizar-State-2015,FourDecades,AlgHierarchy}:
                 We deal with roots and multiple roots of polynomials and show that
                 both the real numbers and finite domains are not algebraically closed.
                 We also prove the identity theorem for polynomials and that the
                 number of multiple roots is bounded by the polynomial's degree \cite{HH90}.}}

@onproceedings{AlgHierarchy,
   author={Grabowski, Adam and Korniłowicz, Artur and Schwarzweller, Christoph},
   title={On algebraic hierarchies in mathematical repository of Mizar},
   booktitle={Proceedings of the 2016 Federated Conference on Computer Science and Information Systems,
              FedCSIS2016, Gda{\'{n}}sk, Poland, September 11--14, 2016},
   editors={Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin}.
   pages={363--371},
   year={2016},
   doi={10.15439/2016F520}}

@BOOK{HH90,
      AUTHOR = {H. Heuser},
      TITLE = {Lehrbuch der Analysis},
      PUBLISHER = {B.G. Teubner Stuttgart},
      YEAR = {1990}}
