Show that $I = \{a +\sqrt2b \in \Bbb Z[\sqrt2] : a$ and $b$ are both multiple of $5\}$ is a maximal ideal.
127237
Let $I = \{a +ib \in \Bbb Z[i] : a$ and $b$ are both multiple of $5\}$.
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
86807
The units of $\mathbb Z[\sqrt{2}]$
93641
A maximal ideal among those avoiding a multiplicative set is prime
50241
Cardinality of the quotient ring $\mathbb Z_5[i]/\langle 1+i\rangle$
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
111996
Maximal and Prime Ideal in Z
111189
Intersection of all maximal ideals containing a given ideal
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
99715
Proper ideal and units proof
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
129371
Maximal ideals in the ring of real functions on $[0,1]$
67203
Complement of maximal multiplicative set is a prime ideal
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )