How do I define all the possible ideals of a given Ring-Set? Example on $Z(m)$. Do I stop when I find enough ideals that their union give's me my given set??
2026-04-23 16:09:58.1776960598
Ideals on Rings?How do i Define them?
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In general the answer to your question is "No": let $R$ be a commutative (to keep things simple) ring. Then every element $x\in R$ yields the principal ideal $Rx$ and the union of all principal ideals equals $R$. However $R$ might possess non-principal ideals.
If by $Z(m)$ you mean the integers modulo $m$, then the answer is "Yes": all ideals of this ring are principal, since the ring itself is a homomorphic image of $\mathbb{Z}$, in which all ideals are principal.