How to prove that a ring is not flat over $k[t,s]$?
53335
Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
141100
Nontrivial subring with unity different from the whole ring?
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?
73689
A question about the equivalence relation on the localization of a ring.
149973
Showing the following coordinate rings are not isomorphic
40996
Proving that free modules are flat (without appealing projective modules)
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
46843
A ring without the Invariant Basis Number property
143429
Kernel of ring homomorphism $k[X,Y] \rightarrow k[t^2, t^3]$
154495
Prove that a nontrivial subring of a ring that is a domain has the same identity
39755
In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
38028
finitely generated k-algebra and polynomial ring
84751
How can it be possible to localize a ring at a set with zero divisors?
32772
Proving units in a ring
94747
Show that the rings $2\mathbb{Z}$ and $3\mathbb{Z}$ are not isomorphic.
6646
A (non-artificial) example of a ring without maximal ideals