๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

On Normal Bases for Finite Commutative Rings

โœ Scribed by Gabriele Steidl

Publisher
John Wiley and Sons
Year
1990
Tongue
English
Weight
920 KB
Volume
145
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

โœฆ Synopsis

This paper is devoted to the introduction of extension rings S := R[z]/gR[z] with a suitable polynomial g 6 R[z] of arbitrary commutative rings R with identity and to the development of a normal basis concept of S over R, which is similar to that of GALOIS extensions of finite fielda. We prove new results for GALOIS extensions of local rings and apply them together with the Chinese remainder theorem to solve the above task in a constructive way.

๐Ÿ“œ SIMILAR VOLUMES

On the Density of Normal Bases in Finite
On the Density of Normal Bases in Finite Fields
โœ Gudmund Skovbjerg Frandsen ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 164 KB

## Let % O L denote the "nite "eld with qL elements, for q a prime power. % O L may be regarded as an n-dimensional vector space over % O . 3% O L generates a normal basis for this vector space (% O L :% O ), if + , O, q , 2 , O L\ , are linearly independent over % O . Let N O (n) denote the numbe