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Remarks on a paper of Guy Henniart
Remarks on a paper of Guy Henniart

... Let K/E be an infinite Galois extension of p-adic local fields. Let v be a jump for the upper numbering filtration and define α = inf{α ∈ R | Gal(K/E)α ⊆ Gal(K/E)v }. Then α is strictly smaller than v. 1.5. Wild, homogeneous local Galois representations All fields are non-Archimedean local containin ...
Morphisms in Logic, Topology, and Formal Concept Analysis
Morphisms in Logic, Topology, and Formal Concept Analysis

... ping on models in the opposite direction, with the property that the image of a formula relates to a given model if and only if the image of the model relates to the formula. These morphisms have several advantages: other than being motivated in logical terms, they can easily be described for arbitr ...
TABLES OF OCTIC FIELDS WITH A QUARTIC SUBFIELD 1
TABLES OF OCTIC FIELDS WITH A QUARTIC SUBFIELD 1

Lecture 1
Lecture 1

... Topology is a generalization of order Verify that for an ordered set (X , 6) the set τ = {A ∈ P(X ) | ∀x∈A ∀y ∈X [(x 6 y ) ⇒ (y ∈ A)]} is a topology on X . It is called the Alexandroff topology of (X , 6). Show that two different orders on the same set give rise to two different Alexandroff topologi ...
CSIS 5857: Encoding and Encryption
CSIS 5857: Encoding and Encryption

... – Compute inverse of that polynomial mod some other “prime” polynomial – Galois Field with m = 28 used to create S-Boxes for AES , mapping 256 possible byte inputs to 256 possible byte outputs ...
1

Galois connection

In mathematics, especially in order theory, a Galois connection is a particular correspondence (typically) between two partially ordered sets (posets). The same notion can also be defined on preordered sets or classes; this article presents the common case of posets. Galois connections generalize the correspondence between subgroups and subfields investigated in Galois theory (named after the French mathematician Évariste Galois). They find applications in various mathematical theories.A Galois connection is rather weak compared to an order isomorphism between the involved posets, but every Galois connection gives rise to an isomorphism of certain sub-posets, as will be explained below.The literature contains two closely related notions of ""Galois connection"". In this article, we will distinguish between the two by referring to the first as (monotone) Galois connection and to the second as antitone Galois connection.The term Galois correspondence is sometimes used to mean bijective Galois connection; this is simply an order isomorphism (or dual order isomorphism, dependently on whether we take monotone or antitone Galois connections).
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