query: Radical of an ideal in a finitely generated ring over $k$ is the intersection of maximal ideals containing it.
positive_passages.docid: 149412
positive_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 133706
negative_passages.text: If R is a local ring, then its maximal left-ideal is a left and right ideal
negative_passages.docid: 139794
negative_passages.text: In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
negative_passages.docid: 112150
negative_passages.text: Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 67669
negative_passages.text: Prime ideals of a finite direct product ring
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 157876
negative_passages.text: If every prime ideal is maximal, what can we say about the ring?
negative_passages.docid: 93723
negative_passages.text: Find all the maximal ideals in the ring $\mathbb{R}[x]$.
negative_passages.docid: 27766
negative_passages.text: Comaximal ideals in a commutative ring
negative_passages.docid: 92822
negative_passages.text: Finite number of elements generating the unit ideal of a commutative ring
negative_passages.docid: 148788
negative_passages.text: Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
negative_passages.docid: 69649
negative_passages.text: If an ideal contains the multiplicative identity, then it is the whole ring
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?