Galois theory about the correspondence between subgroups and subfields, discovered by the French mathematician Évariste Galois. A Galois connection can...

mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental...

as the lower adjoint part of a unique Galois connection. For any pair of preorders X and Y, a Galois connection is given by a pair of monotone functions...

Galois theory is a result that describes the structure of certain types of field extensions in relation to groups. It was proved by Évariste Galois in...

such a more general duality is from Galois theory. For a fixed Galois extension K / F, one may associate the Galois group Gal(K/E) to any intermediate...

way from a suitable Galois connection. The Galois connection is not uniquely determined by the closure operator. One Galois connection that gives rise to...

Ehresmann connection, gives a manner for differentiating sections of a general fibre bundle Electrical connection, allows the flow of electrons Galois connection...

In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the...

}}Y^{c}:=M\backslash Y} . From the above algebras, there exist different types of Galois connections, e.g., (1) X ⊆ Y I {\displaystyle X\subseteq Y^{I}} ⟺ Y ⊆ X I {\displaystyle...

Évariste Galois (1811–1832), a French mathematician. Galois closure Galois cohomology Galois connection Galois correspondence Galois/Counter Mode Galois covering...

associative operators. The lower and upper adjoints in a (monotone) Galois connection, L and G are quasi-inverses of each other; that is, LGL = L and GLG...

mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...

equivalently, its transitive closure is antisymmetric. Adjoint. See Galois connection. Alexandrov topology. For a preordered set P, any upper set O is Alexandrov-open...

elaborate type of functions is given by so-called Galois connections. Monotone Galois connections can be viewed as a generalization of order-isomorphisms...

rephrase the above definition in terms of the existence of suitable Galois connections between related posets — an approach of special interest for category...

graph, and its special case the bipartite double cover Covering group Galois connection Quotient space (topology) Hatcher, Allen (2002). Algebraic topology...

to its inverse Adjoint equation The upper and lower adjoints of a Galois connection in order theory The adjoint of a differential operator with general...

for Galois groups, the real interest lies often in refining a correspondence to a duality (i.e. antitone order isomorphism). A treatment of Galois theory...

subgroups of a quotient group. More generally, there is a monotone Galois connection ( f ∗ , f ∗ ) {\displaystyle (f^{*},f_{*})} between the lattice of...

closure of V is equal to V⊥⊥. The orthogonal complement is thus a Galois connection on the partial order of subspaces of a Hilbert space. In general,...

preserve all suprema/infima can be guaranteed to be part of a unique Galois connection as long as some additional requirements are met. A lattice L is distributive...

intersection of the kernels of the χ with χ(P) = 1. This gives an (antitone) Galois connection between monogenic closed subgroups of T (those with a single generator...

of irreducible closed subsets. This follows immediately from the Galois connection between ideals of R and closed subsets of Spec(R) and the observation...

orthogonal complement generalizes to the annihilator, and gives a Galois connection on subsets of the inner product space, with associated closure operator...

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...

{\displaystyle V\approx V^{**}} . In particular, forming the annihilator is a Galois connection on the lattice of subsets of a finite-dimensional vector space. If...

of the ideal generated by S. In more abstract language, there is a Galois connection, giving rise to two closure operators; they can be identified, and...

and centrally symmetric spherical polyhedra can be extended to a Galois connection including all spherical polyhedra (not necessarily centrally symmetric)...

October 2010. Cousot, P.; Cousot, R. (August 1992). "Comparing the Galois Connection and Widening / Narrowing Approaches to Abstract Interpretation" (PDF)...

if and only if every mapping fa is the lower adjoint of a monotone Galois connection. In this case the respective upper adjoint ga is given by ga(x) =...