query: Question on proof : $I\leq R$ is an ideal s.t. $\sqrt I$ is maximal, then $I$ is primary.
positive_passages.docid: 18406
positive_passages.text: An ideal whose radical is maximal is primary
negative_passages.docid: 111307
negative_passages.text: If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
negative_passages.docid: 87103
negative_passages.text: Quick question about ideals of field $F$ in $F[x]$ are principal.
negative_passages.docid: 80232
negative_passages.text: Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
negative_passages.docid: 93723
negative_passages.text: Find all the maximal ideals in the ring $\mathbb{R}[x]$.
negative_passages.docid: 69352
negative_passages.text: Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
negative_passages.docid: 109199
negative_passages.text: Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
negative_passages.docid: 134939
negative_passages.text: Norm of element $\alpha$ equal to absolute norm of principal ideal $(\alpha)$
negative_passages.docid: 6699
negative_passages.text: An ideal that is maximal among non-finitely generated ideals is prime.
negative_passages.docid: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 43774
negative_passages.text: Given distinct maximal ideals $M_1,...,M_n$, is $M_1\cdots M_n$ radical?
negative_passages.docid: 38228
negative_passages.text: Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
negative_passages.docid: 6307
negative_passages.text: maximal ideal not containing some expression
negative_passages.docid: 74537
negative_passages.text: Maximal Ideals in $K[y]$
negative_passages.docid: 119056
negative_passages.text: If in a UFD every maximal ideal is principal then it is a PID
negative_passages.docid: 92519
negative_passages.text: ideal behind Maximal ideals are Prime ideals
negative_passages.docid: 67203
negative_passages.text: Complement of maximal multiplicative set is a prime ideal