Is the ideal generated by ${4,x}$ a principal ideal in $Z[x]$?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
68202
Must an ideal generated by an irreducible element be a maximal ideal?
113152
Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
49854
Ideals in polynomial rings generated by linear polynomials
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
146801
Primary decomposition of an ideal
65536
Finitely generated ideals in a Boolean ring are principal, why?
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
92822
Finite number of elements generating the unit ideal of a commutative ring
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
78380
Dedekind domain with a finite number of prime ideals is principal