@MISC{FVALUAT1.MIZ,
  AUTHOR = {Bancerek, Grzegorz and Kobayashi, Hidetsune and Korni{\l}owicz, Artur},
  TITLE = {Valuation Theory, Part {I}},
  SECTION1 = {Extended Reals},
  SECTION2 = {Structures},
  SECTION3 = {Valuation},
  SECTION4 = {Valuation Ring},
  DAY = {7},
  MONTH = {April},
  YEAR = {2011},
  ADDRESS1 = {Bia{\l}ystok Technical University},
  ADDRESS2 = {Department of Mathematics\\ College of Science and Technology\\Nihon University\\ 8 Kanda Surugadai Chiyoda-ku, Tokyo\\ 101-8308 Japan},
  ADDRESS3 = {Institute of Informatics\\ University of Bia{\l}ystok\\ Sosnowa 64, 15-887 Bia{\l}ystok\\ Poland},
  SUMMARY = {In the article we introduce a valuation function
  over a field \cite{EmilArtin}. Ring of non-negative elements
  and its ideal of positive elements have been also defined.}}

@BOOK{EmilArtin,
  AUTHOR = {Artin, Emil},
  TITLE = {Algebraic Numbers and Algebraic Functions},
  publisher = {Gordon and Breach Science Publishers},
  year = {1994}}
