Zero product property for integers

[de1irious]

Hi, I am just wondering if the zero product property (ab=0 implies a=0 or b=0) can be proven on the integers, or is it directly axiomatic to the defining of the integers? Also, where might I find a definition of the integer axioms? Thanks a lot,

 

[HallsofIvy]

The "zero product property" is equivalent to the "cancellation" property, if xz= xy and x is not 0, then z= y and you can take either of them as an axiom.

Or you can use "Peano's axioms" and prove either from that.

Wikipedia's article on Peano's axioms is at
http://en.wikipedia.org/wiki/Peano_axioms

Wolfram's is here
http://mathworld.wolfram.com/PeanosAxioms.html