The aim of this work is the construction of a wide class of disconnected locally compact nearfields. They are all Dickson nearfields and derived from local fields by means of couplings described explicitly.

The aim of this paper is the construction of a new class of locally compact nearfields. They are all derived from a local field F by means of certain mappings $$F^*\rightarrow \Delta \le {{\mathrm{Aut}}}\, F$$
 , called couplings on F. Couplings on any field F can be described in terms of crossed homomorphisms $$\Delta \rightarrow F^*/U$$
 , where $$U\le F^*$$
 is invariant under $$\Delta $$
 and $$[F^*:U]=|\Delta |$$
 .

Construction of locally compact nearfields

On Crossed Homomorphisms and the Construction of a New Class of Locally Compact Dickson Nearfields

The aim of this work is the construction of a new class of disconnected locally compact near-fields. They are all Dickson near-fields and derived from finite-dimensional division algebras over local fields by means of strong couplings with a finite Abelian Dickson group consisting of inner automorphisms.

Construction of Locally Compact Near-Fields from $$\mathfrak {p}$$ p -Adic Division Algebras

Number Theory

Part I Algebraic Theory: Cohomology of Profinite Groups.- Some Homological Algebra.- Duality Properties of Profinite Groups.- Free Products of Profinite Groups.- Iwasawa Modules.- Part II Arithmetic Theory: Galois Cohomology.- Cohomology of Local Fields.- Cohomology of Global Fields.- The Absolute Galois Group of a Global Field.- Restricted Ramification.- Iwasawa Theory of Number Fields.- Anabelian Geometry.- Literature.- Index.

Cohomology of number fields

Complete discrete valuation fields Extensions of discrete valuation fields The norm map Local class field theory I Local class field theory II The group of units of local number fields Explicit formulas for the Hilbert symbol Explicit formulas for the Hilbert pairing on formal groups The Milnor $K$-groups of a local field Bibliography List of notations Index

Construction of locally compact nearfields

Citations

On Crossed Homomorphisms and the Construction of a New Class of Locally Compact Dickson Nearfields

Construction of Locally Compact Near-Fields from $$\mathfrak {p}$$ p -Adic Division Algebras

References

Number Theory

Cohomology of number fields

Local Fields and Their Extensions

Theorie der Fastkörper

Unendliche Dicksonsche Fastkörper

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