query: Ideals of $\mathbb Z\times\mathbb F_4$
positive_passages.docid: 16945
positive_passages.text: Finding the Ideals of a Direct Product of Rings
negative_passages.docid: 87103
negative_passages.text: Quick question about ideals of field $F$ in $F[x]$ are principal.
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$
negative_passages.docid: 58425
negative_passages.text: Defining the Product of Ideals
negative_passages.docid: 89313
negative_passages.text: Maximal ideals of polynomial rings in infinitely many variables
negative_passages.docid: 110984
negative_passages.text: Ideals and prime ideals in a commutative ring.
negative_passages.docid: 13717
negative_passages.text: Homomorphisms from $S_4$ to $\mathbb Z_2$
negative_passages.docid: 52966
negative_passages.text: Rings, ideals and units-proof
negative_passages.docid: 72640
negative_passages.text: $(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
negative_passages.docid: 70856
negative_passages.text: Construct ideals in $\mathbb Z[x]$ with a given least number of generators
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 20097
negative_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 70861
negative_passages.text: $\mathbb P^n\times \mathbb P^m\not\cong \mathbb P^{m+n}$
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 31585
negative_passages.text: Primary ideals of $\mathbb{Z}$
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals