query: When is a holomorphy ring a PID?
positive_passages.docid: 153954
positive_passages.text: When a holomorphy ring is a PID?
negative_passages.docid: 26644
negative_passages.text: Does this give a localization of a ring?
negative_passages.docid: 24931
negative_passages.text: Is the localization of a PID a PID?
negative_passages.docid: 93694
negative_passages.text: Boundary behaviour of holomorphic function on unit disk
negative_passages.docid: 115781
negative_passages.text: Proof about Holomorphic functions in the unit disc
negative_passages.docid: 93621
negative_passages.text: Prove that $\mathbb{Z}[\omega]$ is an integral domain
negative_passages.docid: 137045
negative_passages.text: The estimate of real and imaginary part of a holomorphic function
negative_passages.docid: 63446
negative_passages.text: The existence of analytical branch of the logarithm of a holomorphic function
negative_passages.docid: 95408
negative_passages.text: Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
negative_passages.docid: 93658
negative_passages.text: Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
negative_passages.docid: 137379
negative_passages.text: How to get the PID of my script?
negative_passages.docid: 121845
negative_passages.text: Quotient of polynomials, PID but not Euclidean domain?
negative_passages.docid: 85915
negative_passages.text: Principal prime ideals are minimal among prime ideals in a UFD
negative_passages.docid: 92420
negative_passages.text: Characteristic of  a Non-unital Integral Ring
negative_passages.docid: 83014
negative_passages.text: Holomorphic function interpolating $e^{-n}$
negative_passages.docid: 9873
negative_passages.text: GCD in a PID persists in extension domains
negative_passages.docid: 135912
negative_passages.text: why $f$ is holomorphic if $f(z) = \frac{1}{2\pi i} \int_\gamma \frac{f(\zeta)\, d \zeta}{\zeta - z}$?