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There is a page named "Extension field index" on Wikipedia

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  • mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important...
    9 KB (1,444 words) - 10:15, 18 February 2024
  • a finite extension and let w be an extension of v to L. The index of Γv in Γw, e(w/v) = [Γw : Γv], is called the reduced ramification index of w over...
    18 KB (2,370 words) - 15:25, 5 February 2024
  • mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the...
    8 KB (1,100 words) - 22:29, 3 May 2024
  • mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions of local...
    16 KB (2,212 words) - 16:30, 14 July 2024
  • In algebra, a purely inseparable extension of fields is an extension k ⊆ K of fields of characteristic p > 0 such that every element of K is a root of...
    9 KB (1,280 words) - 20:15, 23 January 2024
  • mathematics, an algebraic number field (or simply number field) is an extension field K {\displaystyle K} of the field of rational numbers Q {\displaystyle...
    52 KB (8,365 words) - 00:03, 7 February 2024
  • Life extension is the concept of extending the human lifespan, either modestly through improvements in medicine or dramatically by increasing the maximum...
    113 KB (12,505 words) - 01:28, 3 July 2024
  • Thumbnail for Poincaré–Hopf theorem
    the index for a vector field with nonisolated zeroes. A construction of this index and the extension of Poincaré–Hopf theorem for vector fields with...
    6 KB (867 words) - 12:53, 31 January 2024
  • mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK...
    16 KB (2,533 words) - 16:04, 25 May 2024
  • local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete...
    9 KB (1,047 words) - 04:51, 26 April 2023
  • filename extension, file name extension or file extension is a suffix to the name of a computer file (for example, .txt, .docx, .md). The extension indicates...
    17 KB (2,375 words) - 15:03, 13 June 2024
  • this is a primitive nth root of unity. Then the nth cyclotomic field is the extension Q(ζn) of Q generated by ζn. The nth cyclotomic polynomial Φ n (...
    13 KB (1,713 words) - 20:52, 23 April 2024
  • Thumbnail for Ramification (mathematics)
    set of extensions of a valuation of a field K to an extension field of K. This generalizes the notions in algebraic number theory, local fields, and Dedekind...
    8 KB (1,116 words) - 22:12, 25 January 2023
  • 1971: Isadore Singer proposes a comprehensive program for future extensions of index theory. 1972: Gennadi G. Kasparov publishes his work on the realization...
    53 KB (7,529 words) - 04:31, 30 May 2024
  • fields: Algebraic number field: A finite extension of Q {\displaystyle \mathbb {Q} } Global function field: The function field of an irreducible algebraic...
    8 KB (1,054 words) - 14:30, 11 June 2024
  • Victor (2001) [1994], "Index theory", Encyclopedia of Mathematics, EMS Press: "The main question in index theory is to provide index formulas for classes...
    43 KB (7,001 words) - 21:10, 13 July 2024
  • Windows Shell Extensions, MSDN Magazine, June 2000, archived from the original on August 31, 2004, retrieved August 26, 2007 "What is Indexing Service?"....
    64 KB (6,809 words) - 10:58, 26 May 2024
  • values are little-endian; field and subfield numbers are per Version 2.0 of the specification. Version 2 added the extension area and footer. The developer...
    14 KB (1,728 words) - 20:00, 19 June 2024
  • Thumbnail for List of HTTP header fields
    HTTP header fields are a list of strings sent and received by both the client program and server on every HTTP request and response. These headers are...
    53 KB (2,473 words) - 11:35, 7 July 2024
  • (Shimura & Taniyama 1961). A number field K is a CM-field if it is a quadratic extension K/F where the base field F is totally real but K is totally imaginary...
    5 KB (718 words) - 12:11, 8 November 2023
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