Nettet12. jan. 2024 · In the present paper, we give a simpler description of the obstruction group. It is also shown that if the étale algebra is a product of pairwise linearly disjoint field extensions, then the Hasse principle holds, and that if an embedding exists after an odd degree extension, then it also exists over the global field itself. Nettet31. okt. 2024 · 1 Answer. Thanks to Arno Fehm's observation above, the answer in the general case is NO. In the number field case, R = O K and S = O F (or overrings thereof in K resp. F ), and we can argue as follows. Let p Z = p ∩ Z. Let q 1, ⋯, q s be the rational primes that ramify in F. If not on the list, include p as well.
Regular extension - Wikipedia
NettetIn field theory, a branch of algebra, a field extension / is said to be regular if k is algebraically closed in L (i.e., = ^ where ^ is the set of elements in L algebraic over k) and L is separable over k, or equivalently, ¯ is an integral domain when ¯ is the algebraic closure of (that is, to say, , ¯ are linearly disjoint over k).. Properties ... Nettetin the field extensions not occurring in abelian groups. 1. Preliminaries; modular extensions, Theorem 1.1. Let K and ILa} be subfields of some common field, and suppose K is linearly disjoint from each La. Then K is linearly disjoint from L = nLLa Proof. Suppose that there are xl, , xn in L linearly independent over L n K but not over K. drove herself to madness with a silver spoon
THE ORDER OF INSEPARABILITY OF FIELDS - cambridge.org
Nettetof all extensions of degree at most d of a number field. In [CZ11] and [Che13] it is proved that a Galois extension of a number field has uniformly bounded local degrees if and only if its Galois group has finite exponent. So, for a Galois extension, the uniform boundedness of the local degrees translates into a property of its Galois group. Nettetdiscussion )ִדיּּון (ז disjoint )זָר (ת disjoint union ִחתּוְך זָר linearly disjoint ֵָּאריתִ מֻ פְ ָרד לִ ינ disjunction ) ִדסְ יּונ ְְקצְ יָה (נ,)בְּ ֵּר ָרה (נ distance )מֶ ְרחָ ק (ז distribution )הִ תְ פַ לְ גּות (נ bounded distribution הִ תְ ... NettetWere it a field, then its only ideals were itself or 0, then since the map is surjective, its kernel cannot be everything, then it is 0 and again we have an isomorphism, implying … collections made easy