@article{RING_3.MIZ,
  AUTHOR = {Schwarzweller, Christoph and Korni{\l}owicz, Artur},
  TITLE = {Characteristic of Rings; Prime Fields},
  ADDRESS1 = {Institute of Informatics, University of Gda{\'n}sk, Poland},
  ADDRESS2 = {Institute of Informatics, University of Bia{\l}ystok, Poland},
  SECTION1 = {Preliminaries},
  SECTION2 = {Properties of Fractions},
  SECTION3 = {Preliminaries about Rings and Fields},
  SECTION4 = {Embedding the Integers in Rings},
  SECTION5 = {Mono- and Isomorphisms of Rings},
  SECTION6 = {Characteristic of Rings},
  SECTION7 = {Prime Fields},
  DAY = {14},
  MONTH = {August},
  YEAR = {2015},
  MSC2010 = {03B35},
  KEYWORDS = {commutative algebra, characteristic of rings, prime field},
  SUMMARY = {The notion of the characteristic of rings and its basic properties are formalized
  \cite{Jacobson2009}, \cite{Waerden2003}, \cite{Luneburg1999}.
  Classification of prime fields in terms of isomorphisms with
  appropriate fields ($\mathbb{Q}$ or $\mathbb{Z}/p$) are presented.
  To facilitate reasonings within the field of rational numbers,
  values of numerators and denominators of basic operations over rationals are computed.},
  }
