Abstract/Details

## ON FUNDAMENTAL SETS OVER A FINITE FIELD

ABBAS, YOUSEF HASAN.
University of South Florida ProQuest Dissertations Publishing,  1984. 8427953.

### Abstract (summary)

A partition over a finite field is defined and each equivalence class (fundamental class) is constructed and represented by a set called a fundamental set. If a primitive element is used to construct the addition table over one fundamental set of each fundamental class, then all additions over the field can be computed. The number of fundamental classes is given for some finite fields. The solutions of P(x) = x('p('n)) + ax + b, P(x) (ELEM) Z(,p){x} in the field are discussed.

This partition is extended to define a new equivalence relation over fundamental classes to minimize the computational time and the number of fundamental sets required to carry out the additions over the field. Some results on the solutions of the trinomial h(x) = x('p('(lamda))) + ax + b (ELEM) Z{x} are discussed.

The additive subgroups of a field are discussed and a construction method is developed by using the fundamental sets. The number of additive subgroups is given under certain conditions.

### Indexing (details)

Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
ON FUNDAMENTAL SETS OVER A FINITE FIELD
Author
ABBAS, YOUSEF HASAN
Number of pages
70
Degree date
1984
School code
0206
Source
DAI-B 45/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9798413106488
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8427953
ProQuest document ID
303322827