Why proper ideal doesn't contain $1$?
69649
If an ideal contains the multiplicative identity, then it is the whole ring
112043
Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
45575
why each left ideal of this is minimal?
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
33576
Non-principal ideal in $K[x,y]$?
59411
Primary ideals confusion with definition
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
148208
In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
140553
An ideal which is not finitely generated
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
105313
Existence of minimal prime ideal contained in given prime ideal and containing a given subset
155745
Ideals of $\mathbb{Z}[X]$
9204
Counterexamples to the avoidance lemma for arbitrary ideals
149136
On the height of an ideal
31585
Primary ideals of $\mathbb{Z}$
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$