query: Prime ideal splitting in field extension and its normal closure
positive_passages.docid: 145594
positive_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 111114
negative_passages.text: Prove that an ideal in $k[x,y]$ is a prime ideal
negative_passages.docid: 155771
negative_passages.text: Product of degree of two field extensions of prime degree
negative_passages.docid: 147871
negative_passages.text: How do the prime ideals of $\mathbb{Z}_{k}$ look like?
negative_passages.docid: 115449
negative_passages.text: Inclusion of Fields whose order is a prime power
negative_passages.docid: 58425
negative_passages.text: Defining the Product of Ideals
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 80538
negative_passages.text: Fields extensions over isomorphic fields of different degrees
negative_passages.docid: 1060
negative_passages.text: Minimal polynomial of intermediate extensions under Galois extensions.
negative_passages.docid: 3604
negative_passages.text: If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
negative_passages.docid: 117536
negative_passages.text: Why is the localization at a prime ideal a local ring?
negative_passages.docid: 93641
negative_passages.text: A maximal ideal among those avoiding a multiplicative set is prime
negative_passages.docid: 57283
negative_passages.text: Extending Homomorphism into Algebraically Closed Field
negative_passages.docid: 102341
negative_passages.text: Primary decomposition of a monomial ideal
negative_passages.docid: 94157
negative_passages.text: Normal Ring and Prime Ideal whose Square is Principal
negative_passages.docid: 85915
negative_passages.text: Principal prime ideals are minimal among prime ideals in a UFD