Field is an algebraic structure defined as 7-tuple of set, binary operations on this set (addition and multiplication), two unary operations (multiplicative inverse) and two nullary operations (0 and 1). With folowing axioms:
associativity of addition and multiplication
commutativity of addition and multiplication
0 and 1 are additive and multiplicative identity, it means that a + 0 = a and a· 1 = a for all a from field
for additive inverse (-a) holds: a + (−a) = 0
for multiplicative inverse (a^(-1)) holds: a· a−1 = 1
distributivity of multiplication over addition: a· (b + c) = (a· b) + (a· c)