Physical Sciences and Mathematics Commons^™

The Galois Group Of A Polynomial Equation With Coefficients In A Finite Field, Charles Leston Bradshaw

Masters Theses

Introduction [Abbreviated]:

The primary purpose of this thesis is to demonstrate a method for the determination of the Galois group of a polynomial equation with coefficients in a finite field. The problem of finding the Galois group of an arbitrary equation, where the coefficient field is either finite or infinite, is neither new nor unsolved.

Prime Ideals In Semigroups, Helen Bradley Grimble

Masters Theses

The concept of prime ideal, which arises in the theory of rings as a generalization of the concept of prime number in the ring of integers, plays a highly important role in that theory, as might be expected from the central position occupied by the primes in arithmetic. In the present paper, the concept is defined for ideals in semigroups, the simplest of the algebraic systems of single composition, and some analogies and differences between the ring and semigroup theories are brought out. We make only occasional references to ring theory, however; a reader acquainted with that theory will …