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Let / be a finite Galois extension of nonarchimedean local fields with finite residue fields / and Galois group.Then the following are equivalent. (i) / is unramified. (ii) / is a field, where is the maximal ideal of .
In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains. [1] [2] The structure of the set of extensions is known better when L/K is Galois.
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With a legacy of more than 100 years, the Better Business Bureau (BBB) is the go-to watchdog for evaluating businesses and charities. The nonprofit organization maintains a massive database of ...
The splitting of prime ideals in Galois extensions is sometimes attributed to David Hilbert by calling it Hilbert theory. There is a geometric analogue, for ramified coverings of Riemann surfaces, which is simpler in that only one kind of subgroup of G need be considered, rather than two. This was certainly familiar before Hilbert.
Labor unions and critics of the extensions often point to the large profits that some hospitals reap: A California Health Care Foundation report published in August found that California’s ...
In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field.. More precisely, Abhyankar's lemma states that if A, B, C are local fields such that A and B are finite extensions of C, with ramification indices a and b, and B is tamely ramified over C and b divides a, then the compositum AB is an unramified ...
Fitch Ratings; Rating Date Ref. Alabama: AA Aa1 [2] AA+ May 10, 2022 [3] Alaska: AA- Aa3 [2] [4] A+ April 13, 2022 [5] Arizona: AA Aa1 [2] — [6] Arkansas: AA Aa1 [2] — California: AA- Aa2 [2] AA March 1, 2022 [7] Colorado: AA Aa1 [2] — [8] Connecticut: A Aa3 [2] [9] AA- May 24, 2022 [10] Delaware: AAA Aaa [2] [11] AAA February 9, 2022 [12 ...