@MISC{REALSET2.MIZ,
  AUTHOR = {Bia{\l}as, J\'ozef},
  TITLE = {Properties of Fields},
  DAY = {20},
  MONTH = {June},
  YEAR = {1990},
  ADDRESS1 = {University of {\L}\'od\'z},
  SUMMARY = {    The second part of considerations concerning
groups and fields. It includes a definition and properties of
commutative field  $F$  as a structure defined by: the set, a support
of $F$,  containing 
two different elements, by two binary operations
 ${\bf +}_{F}$, ${\bf \cdot}_{F}$ on this 
set, called addition and multiplication, and by two elements from
the support of $F$,
 ${\bf 0}_{F}$  being neutral for addition and
 ${\bf 1}_{F}$  being neutral for
multiplication. This structure is named a field if
 $\langle$the support of $F$, ${\bf +}_{F}$, ${\bf 0}_{F} \rangle$
and
 $\langle$the support of $F$, ${\bf \cdot}_{F}$, ${\bf 1}_{F} \rangle$
are commutative groups and multiplication
has the property of left-hand and right-hand distributivity with respect to
addition. It is demonstrated that the field  $F$  satisfies the definition of
a field in the axiomatic approach.}}

