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...

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...

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...

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

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

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

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

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

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

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...

}}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...

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...

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

Galois connection between sets of objects and of attributes. This is why in French a concept lattice is sometimes called a treillis de Galois (Galois...

completeness properties is provided through the concept of (monotone) Galois connections, i.e. adjunctions between partial orders. In fact this approach offers...

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...

was a Norwegian mathematician known for his work in ring theory, Galois connections, graph theory, and the history of mathematics. Ore graduated from...

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...

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

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

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...

notions that relate to order isomorphisms are order embeddings and Galois connections. The idea of isomorphism can be understood for finite orders in terms...

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

let Al denote the set of lower bounds of A. (These operators form a Galois connection.) Then the Dedekind–MacNeille completion of S consists of all subsets...

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

residual form a Galois connection under the (more recent) monotone definition of that concept, and for every (monotone) Galois connection the lower adjoint...