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Full-Text Articles in Physical Sciences and Mathematics
The Galois Group Of A Polynomial Equation With Coefficients In A Finite Field, Charles Leston Bradshaw
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
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 …
Constant Rank Matrices, Harlan D. Mills
Constant Rank Matrices, Harlan D. Mills
The Harlan D. Mills Collection
A matrix is a rectangular array of quantities which, as an array, obeys certain rules when combined with other matrices by the operations of addition and multiplication, or when combined with scalar quantities by the operation of multiplication. These operations have meaning if and only if the matric quantities and scalar quantities are elements of a ring. A minor of a matrix is a certain function of a square sub-array of the matrix, and has a unique meaning if and only if the elements of the sub-array are commutative. The rank of a matrix is a function of all possible …