scholarly journals Non-linear group actions with polynomial invariant rings and a structure theorem for modular Galois extensions

2011 ◽  
Vol 103 (5) ◽  
pp. 826-846 ◽  
Author(s):  
Peter Fleischmann ◽  
Chris Woodcock
Keyword(s):  
Linear Group ◽  
Structure Theorem ◽  
Group Actions ◽  
Polynomial Invariant ◽  
Galois Extensions ◽  
Invariant Rings ◽  
Non Linear

scholarly journals On central commutator Galois extensions of rings

2000 ◽  
Vol 24 (5) ◽  
pp. 289-294
Author(s):  
George Szeto ◽  
Lianyong Xue
Keyword(s):  
Automorphism Group ◽  
Galois Group ◽  
Group Ring ◽  
Galois Extension ◽  
Structure Theorem ◽  
Projective Group ◽  
Galois Extensions ◽  
Separable Extensions

LetBbe a ring with1,Ga finite automorphism group ofBof ordernfor some integern,BGthe set of elements inBfixed under each element inG, andΔ=VB(BG)the commutator subring ofBGinB. Then the type of central commutator Galois extensions is studied. This type includes the types of Azumaya Galois extensions and GaloisH-separable extensions. Several characterizations of a central commutator Galois extension are given. Moreover, it is shown that whenGis inner,Bis a central commutator Galois extension ofBGif and only ifBis anH-separable projective group ringBGGf. This generalizes the structure theorem for central Galois algebras with an inner Galois group proved by DeMeyer.

scholarly journals The invariants of orthogonal group actions

1993 ◽  
Vol 48 (2) ◽  
pp. 313-319 ◽  
Author(s):  
Li Chiang ◽  
Yu-Ching Hung
Keyword(s):  
Quadratic Form ◽  
Finite Field ◽  
Rational Function ◽  
Linear Group ◽  
Function Field ◽  
Orthogonal Group ◽  
Group Actions ◽  
Rational Function Field ◽  
Transcendental Extension

Let Fq be the finite field of order q, an odd number, Q a non-degenerate quadratic form on , O(n, Q) the orthogonal group defined by Q. Regard O(n, Q) as a linear group of Fq -automorphisms acting linearly on the rational function field Fq(x1, …, xn). We shall prove that the invariant subfield Fq(x1,…, xn)O(n, Q) is a purely transcendental extension over Fq for n = 5 by giving a set of generators for it.

Group actions and non-linear sigma models

1990 ◽  
Vol 238 (1) ◽  
pp. 75-80 ◽  
Author(s):  
George Papadopoulos
Keyword(s):  
Sigma Models ◽  
Group Actions ◽  
Non Linear ◽  
Linear Sigma Models

The structure of a partial Galois extension II

2016 ◽  
Vol 15 (04) ◽  
pp. 1650061 ◽  
Author(s):  
Jung-Miao Kuo ◽  
George Szeto
Keyword(s):  
Finite Group ◽  
Galois Extension ◽  
Structure Theorem ◽  
Galois Extensions ◽  
Partial Action ◽  
A Finite Group ◽  
Partial Galois Extension

Let [Formula: see text] be a partial Galois extension where [Formula: see text] is a partial action of a finite group on a ring [Formula: see text] such that the associated ideals are generated by central idempotents. We determine the set of all Galois extensions in [Formula: see text], and give an orthogonality criterion for nonzero elements in the Boolean semigroup generated by those central idempotents. These results lead to a structure theorem for [Formula: see text].

scholarly journals The invariants of projective linear group actions

1989 ◽  
Vol 39 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Huah Chu ◽  
Ming-Chang Kang ◽  
Eng-Tjioe Tan
Keyword(s):  
Rational Function ◽  
Linear Group ◽  
Function Field ◽  
Group Actions ◽  
Direct Computation ◽  
Rational Function Field ◽  
Projective Linear Group

Let Fq be the field with q elements and let G = PGLn(Fq) or PSLn(Fq) act on Fq(x1,…,xn−1), the rational function field of n − 1 variables. Then Fq(x1,…,xn−1)G is purely transcendental over Fq. In fact, a set of n − 1 generators of Fq(x1,…xn−1)G, over Fq is exhibited. The case n = 2 is treated by direct computation.

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