Results 21 to 30 of about 408 (185)

Separable subalgebras of a class of Azumaya algebras

International Journal of Mathematics and Mathematical Sciences, 1998
Let S be a ring with 1, C the center of S, G a finite automorphism group of S of order n invertible in S, and SG the subnng of elements of S fixed under each element in G. It is shown that the skew group ring S*G is a G′-Galois extension of (S*G)G′ that
George Szeto
doaj   +1 more source

The Boolean algebra of Galois algebras

International Journal of Mathematics and Mathematical Sciences, 2003
Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(x)b for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}.
George Szeto, Lianyong Xue
doaj   +1 more source

On automorphism group of free quadratic extensions over a ring

International Journal of Mathematics and Mathematical Sciences, 1984
Let R be a ring with 1, ρ an automorphism of R of order 2. Then a normal extension of the free quadratic extension R[x,ρ] with a basis {1,x} over R with an R-automorphism group G is characterized in terms of the element (x−(x)α) for α in G.
George Szeto
doaj   +1 more source

Parametric Galois extensions

Journal of Algebra, 2015
Given a field $k$ and a finite group $H$, {\it{an $H$-parametric extension over $k$}} is a finite Galois extension of $k(T)$ of Galois group containing $H$ which is regular over $k$ and has all the Galois extensions of $k$ of group $H$ among its specializations.
openaire   +2 more sources

On finite arithmetic groups [PDF]

International Journal of Group Theory, 2013
Let $F$ be a finite extension of $Bbb Q$, ${Bbb Q}_p$ or a globalfield of positive characteristic, and let $E/F$ be a Galois extension.We study the realization fields offinite subgroups $G$ of $GL_n(E)$ stable under the naturaloperation of the Galois ...
Dmitry Malinin
doaj  

Lattice-Valued Topological Systems as a Framework for Lattice-Valued Formal Concept Analysis

Journal of Mathematics, 2013
Recently, Denniston, Melton, and Rodabaugh presented a new categorical outlook on a certain lattice-valued extension of Formal Concept Analysis (FCA) of Ganter and Wille; their outlook was based on the notion of lattice-valued interchange system and a ...
Sergey A. Solovyov
doaj   +1 more source

Norms in finite galois extensions of the rationals

International Journal of Mathematics and Mathematical Sciences, 1990
We show that under certain conditions a rational number is a norm in a given finite Galois extension of the rationals if and only if this number is a local norm at a certain finite number of places in a certain finite abelian extension of the rationals.
Hans Opolka
doaj   +1 more source

Interpretations and Differential Galois Extensions

International Mathematics Research Notices, 2016
We give model theoretic accounts and proofs of the existence and uniqueness of differential Galois extensions with no new constants, for logarithmic differential equations over a differential field K, when the field C of constants of K is not necessarily algebraically closed, under a variety of assumptions on C and K.
Kamensky, Moshe, Pillay, Anand
openaire   +2 more sources

On the Existential Theory of the Completions of a Global Field

Mathematische Nachrichten, EarlyView.
ABSTRACT We discuss the common existential theory of all or almost all completions of a global function field.
Philip Dittmann, Arno Fehm
wiley   +1 more source

A History of Selected Topics in Categorical Algebra I: From Galois Theory to Abstract Commutators and Internal Groupoids [PDF]

Categories and General Algebraic Structures with Applications, 2016
This paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical Galois theory and involves generalized central extensions, commutators, and internal groupoids in Barr exact Mal’tsev and more ...
George Janelidze
doaj