query: A subset of a polynomial ring and its ideal.
positive_passages.docid: 148788
positive_passages.text: Polynomial ring ideal. Show that $(f) \cap R_N = (0) \iff f \notin R_N$
negative_passages.docid: 1719
negative_passages.text: Ideals in the ring of Gaussian integers
negative_passages.docid: 50908
negative_passages.text: Showing a Ring and an Ideal are equal
negative_passages.docid: 87780
negative_passages.text: Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
negative_passages.docid: 148208
negative_passages.text: In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
negative_passages.docid: 5360
negative_passages.text: Ideal contained in a finite union of prime ideals
negative_passages.docid: 83009
negative_passages.text: Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
negative_passages.docid: 35222
negative_passages.text: Characterizing units in polynomial rings
negative_passages.docid: 89313
negative_passages.text: Maximal ideals of polynomial rings in infinitely many variables
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 89864
negative_passages.text: Units in finite polynomial rings
negative_passages.docid: 91180
negative_passages.text: Show $R \setminus S$ is a union of prime ideals
negative_passages.docid: 100553
negative_passages.text: Complement of a prime ideal is a subset closed under multiplication, containing 1
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal