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Y by felixgotti
If is an intergral domain then is too,
Let such that they are non zero, denote
Taking let be the leading coefficient of . Notice that thus so in short for the leading coefficient of cannot be thus must be an integral domain.
Going the other way say is an integral domain,
For the sake of contradiction let such that and , let taking there product,
This contradicts our previous statement thus is an integral domain!
Finally iff is an integral domain then must also be an integral domain
Let such that they are non zero, denote
Taking let be the leading coefficient of . Notice that thus so in short for the leading coefficient of cannot be thus must be an integral domain.
Going the other way say is an integral domain,
For the sake of contradiction let such that and , let taking there product,
This contradicts our previous statement thus is an integral domain!
Finally iff is an integral domain then must also be an integral domain