I've : $I=<p,x>$ is not a principal ideal in $Z[x]$ where p is prime. My question : Is $I=<p,x>$ a principal ideal in $Z[x]$ where p is not a prime? More particularly, is the ideal generated by ${4,x}$ a principal ideal in $Z[x]$ ?
Is the ideal generated by ${4,x}$ a principal ideal in $Z[x]$?
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abstract-algebra
ring-theory
ideals
principal-ideal-domains