If $M_1$ and $M_2$ are distinct maximal ideals of, then $R/M_1 \otimes _R R/M_2=0$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
104377
Maximal Ideals in Ring of Continuous Functions
7833
Ideal and minimal polynomial
54345
Prove if a non-trivial ring $R$ has a unique maximal left ideal $J$ , then $J$ is two-sided and is also the unique maximal right ideal in $R$.
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
49521
In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
27766
Comaximal ideals in a commutative ring
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
129371
Maximal ideals in the ring of real functions on $[0,1]$
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
63207
Zorn's lemma and maximal ideals
50445
Explaining the product of two ideals
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?