Browsing by Author "Albu, Toma"

Now showing 1 - 4 of 4

Citation - WoS: 2
Infinite Cogalois Theory, Clifford Extensions, and Hopf Algebras
(World Scientific Publ Co Pte Ltd, 2003) Albu, Toma
The aim of this paper is to present some connections of infinite Cogalois Theory with Clifford extensions and Hopf algebras.
Citation - WoS: 3
Lattice-Isomorphic Groups, and Infinite Abelian g-cogalois Field Extensions
(World Scientific Publ Co Pte Ltd, 2002) Albu, Toma; Basarab, Serban
The aim of this paper is to provide a proof of the following result claimed by Albu (Infinite field extensions with Galois-Cogalois correspondence (II), Revue Roumaine Math. Pures Appl. 47 (2002), to appear): The Kneser group Kne(E/F) of an Abelian G-Cogalois extension E/F and the group of continuous characters Ch(Gal(E/F)) of its Galois group Gal(E/F) are isomorphic (in a noncanonical way). The proof we give in this paper explains why such an isomorphism is expected, being based on a classical result of Baer (Amer. J. Math. 61 (1939), 1-44) devoted to the existence of group isomorphisms arising from lattice isomorphisms of their lattices of subgroups.
Citation - WoS: 2
On Radical Field Extensions of Prime Exponent
(World Scientific Publ Co Pte Ltd, 2002) Albu, Toma
In this paper we investigate finite separable radical extensions K subset of L of prime exponent via the concept of G-Cogalois extension. As particular cases we retrieve some older results in I. Kaplansky [9] and A. Baker and H. M. Stark [7] concerning such radical extensions.
Citation - WoS: 6
Some Examples in Cogalois Theory With Applications To Elementary Fleld Arithmetic
(World Scientific Publ Co Pte Ltd, 2002) Albu, Toma
The aim of this paper is to provide some examples in Cogalois Theory showing that the property of a field extension to be radical (resp. Kneser, or Cogalois) is not transitive and is not inherited by subextensions. Our examples refer especially to extensions of type Q(root r + root d)/Q. We also effectively calculate the Cogalois groups of these extensions. A series of applications to elementary arithmetic of fields, like: for what n, d is an element of N* is root n + root d a sum of radicals of positive rational numbers when is (n0)root a(0) a finite sum of monomials of form c center dot(n1)root a(1)(j1) ... (nr)root a(r)(jr), where r, j(1), ... , j(r) is an element of N*, c is an element of Q*, and a(0), ... , a(r) is an element of Q(+)(*) are also presented.