query: Ring Inside an Algebraic Field Extension
positive_passages.docid: 28313
positive_passages.text: Intermediate ring between a field and an algebraic extension.
negative_passages.docid: 83115
negative_passages.text: A set of elements in a reduced unity ring
negative_passages.docid: 98818
negative_passages.text: Quotient ring of a localization of a ring
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 48093
negative_passages.text: Irreducible polynomial in field extension
negative_passages.docid: 153589
negative_passages.text: Integral basis of an extension of number fields
negative_passages.docid: 22610
negative_passages.text: Polynomial rings in infinitely indeterminants
negative_passages.docid: 112099
negative_passages.text: Polynomial ring with integral coefficients is integral
negative_passages.docid: 74663
negative_passages.text: Is $\mathbb{R}$ an algebraic extension of some proper subfield?
negative_passages.docid: 63390
negative_passages.text: Infinite algebraic extensions of $\mathbb{Q}$
negative_passages.docid: 104233
negative_passages.text: Is the ring of the polynomials on a finite algebraic set always a product of local rings?
negative_passages.docid: 39755
negative_passages.text: In a faithfully flat ring extension, is $\operatorname{ht}I=\operatorname{ht}IS$ right?
negative_passages.docid: 21604
negative_passages.text: A complete ring with respect to an ideal
negative_passages.docid: 3129
negative_passages.text: A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
negative_passages.docid: 63192
negative_passages.text: A chain ring with Krull dimension greater than one
negative_passages.docid: 80295
negative_passages.text: Field extensions and algebraic/transcendental elements
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$