Prove $I$ is non-principal ideal of $\mathbb{Z}[x]$?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
99423
Is it true every ideal of $\mathbb{Z}[x]$ is finitely generated?
117786
Show that some monomial ideal is primary
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
128711
$(\Bbb Z\oplus \Bbb Z)[X] \not\cong \Bbb Z[X]\oplus \Bbb Z[X]\,$?
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
133561
show that if $K$ is a field then $K[x]$ is principal
250
An irreducible $f\in \mathbb{Z}[x]$, whose image in every $(\mathbb{Z}/p\mathbb{Z})[x]$ has a root?
64130
Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
99198
Principal ideal and free module
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
19310
Identify the ring $\mathbb{Z}[x]/(2x)$
138258
What is the injective envelope of $\mathbb{Z}/n\mathbb{Z}$?
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
57310
Prove $\mathbb{Z}$ is not a vector space over a field
33245
Show that every ideal of the ring $\mathbb Z$ is principal