Exercise
14
[203] Consider the property
\[ \forall x,y\in A~ ,~ x\cdot y=0 \Rightarrow x=0\lor y=0 \]
this property may be false in a ring \(A\); if it holds in a specific ring, then this ring is said to be an integral domain [ 38 ] .
Show that a field \(F\) is always an integral domain. Consequently \(F⧵\{ 0\} \) is a commutative group for multiplication.
Solution
1