query: Prove the module of a holomorphic function cannot be $\frac{K}{\cosh x}$
positive_passages.docid: 148512
positive_passages.text: No analytic function $f$ has modulus $|f(z)|=1/\cosh(\Re z)$
negative_passages.docid: 158502
negative_passages.text: Showing $\sin(\bar{z})$ is not analytic at any point of $\mathbb{C}$
negative_passages.docid: 95942
negative_passages.text: $k[x]/(x^n)$ module with finite free resolution is free
negative_passages.docid: 30511
negative_passages.text: Monic $f(x)\in\Bbb Z[x]$ has no rational root if $f(0)\ \&\ f(1)$ odd [Parity Root Test, Modular Root Test]
negative_passages.docid: 112501
negative_passages.text: A funtion and its fourier transformation cannot both be compactly supported unless f=0
negative_passages.docid: 33338
negative_passages.text: Problem on $\operatorname{Hom}(\mathbb Z_6,R^*\oplus C^*)$
negative_passages.docid: 22529
negative_passages.text: The support of a non finitely generated module
negative_passages.docid: 79056
negative_passages.text: Prove that $\mathbb Z^n$ is not isomorphic to $\mathbb Z^m$ for $m\neq n$
negative_passages.docid: 64130
negative_passages.text: Prove that $\mathbb{Q}^{\times}$ not isomorphic to $\mathbb{Z}^{n}$
negative_passages.docid: 12525
negative_passages.text: complex conjugates of holomorphic functions
negative_passages.docid: 156679
negative_passages.text: $K[X,Y]/(XY-1)$ not isomorphic to $K[T]$
negative_passages.docid: 18484
negative_passages.text: Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
negative_passages.docid: 42652
negative_passages.text: Must $k$-subalgebra of $k[x]$ be finitely generated?
negative_passages.docid: 43136
negative_passages.text: Branch of the n-th root of a holomorphic function is holomorphic
negative_passages.docid: 83595
negative_passages.text: Proving that $\mathbb{A}=\{\alpha \in \mathbb{C}: \alpha \text{ is algebraic over } \mathbb{Q} \}$ is not a finite extension
negative_passages.docid: 135955
negative_passages.text: Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
negative_passages.docid: 148118
negative_passages.text: Prove that field of complex numbers cannot be equipped with an order relation