Find an example of a commutatice unital ring $R$ and an $R$-module such that $\text{Ass}(M)=\emptyset$
86724
Example of a non-zero module that has no associated primes
46717
If $M$ is a Noetherian $R$-module, then $R/\text{Ann}(M)$ is a Noetherian ring
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
75641
Is there a (f.g., free) module isomorphic to a quotient of itself?
126331
Associative ring with identity, inverses, divisors of zero and Artinianity
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
92420
Characteristic of  a Non-unital Integral Ring
33611
necessary and sufficient condition for trivial kernel of a matrix over a commutative ring
45627
Find a sub-ring of M(2, $\mathbb{Q}$) which is isomorphic to $\mathbb{Q}$
83115
A set of elements in a reduced unity ring
10908
Associated elements in a ring
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
37410
Example of a ring with an infinite inclusion chain of ideals
119067
Basic Ring Theory Question involving the unit element
80088
What possible characteristics may a local commutative unital ring have?
35222
Characterizing units in polynomial rings