# On Galois matrix extensions of high order

## Main Article Content

## Abstract

Let *R* be a commutative ring with 1 and *A* a central *R*-Galois algebra with an inner Galois group *G* of order *n* for some integer *n*. Let *M*_{m}(*R*) be the ring of *m* × *m*-matrices over *R* for an integer *m*. Then *M*_{m}(*R*) is also a central Galois *R*-algebra with an inner Galois group for each *m* = *n*^{(2i)} where *i* is a non-negative integer. In particular, 2 is invertible in *R* if and only if *M*_{m}(*R*) is a central Galois *R*-algebra with an inner Galois group for each *m* = *2*^{(2i)} where *i* is a non-negative integer.

## Article Details

How to Cite

*Gulf Journal of Mathematics*,

*2*(3). Retrieved from https://gjom.org/index.php/gjom/article/view/226

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