query: A Cyclic Extension of degree 4 does not contain $i$
positive_passages.docid: 142488
positive_passages.text: Galois Basic Question (Cyclic Order 4 Extension of Q cannot contain i)
negative_passages.docid: 51861
negative_passages.text: $S_4$ is not isomorphic to $D_{12}$
negative_passages.docid: 112933
negative_passages.text: Show that $Z\times Z$ is not cyclic...
negative_passages.docid: 26999
negative_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 116955
negative_passages.text: Showing the existence of a certain kind of extension of a finitely generated algebra
negative_passages.docid: 31511
negative_passages.text: A finite abelian group that does not contain a subgroup isomorphic to $\mathbb Z_p\oplus\mathbb Z_p$, for any prime $p$, is cyclic.
negative_passages.docid: 146617
negative_passages.text: A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
negative_passages.docid: 151786
negative_passages.text: Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
negative_passages.docid: 134342
negative_passages.text: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
negative_passages.docid: 119545
negative_passages.text: Nonzero rationals under multiplication are not a cyclic group
negative_passages.docid: 85586
negative_passages.text: Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
negative_passages.docid: 87238
negative_passages.text: $(1 2)(3 4)$ does not commute with any nonidentity element of odd order in $A_5$.
negative_passages.docid: 24919
negative_passages.text: $\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
negative_passages.docid: 152954
negative_passages.text: Extensions of finite cyclic groups
negative_passages.docid: 107370
negative_passages.text: An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
negative_passages.docid: 125604
negative_passages.text: Proof that $\mathbb{Z}$ has no zero divisors
negative_passages.docid: 128732
negative_passages.text: $\mathbb Z_{p^n}$ is not the direct product of any family of its proper subgroups