Question related to Ideals of the ring of all functions from the set $\{1,2, \dots , 10\}$ to $\mathbb Z_2 $.
87617
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Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
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Finding generator for the ideal generated by $a$ and $b$ in an euclidean domain
47134
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92822
Finite number of elements generating the unit ideal of a commutative ring
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Show that the ideal $ (2, 1 + \sqrt{-7} ) $ in $ \mathbb{Z} [\sqrt{-7} ] $ is not principal
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
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 $\mathbb Z$?
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Ideal Generated by the Union of Two Ideals
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Is $\mathbb{Z}[x]$ a principal ideal domain?
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Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
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Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
16945
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Find generators of the ideal of an algebraic set
17139
Ring of holomorphic functions