Prime Ideals in Semigroups

Author

Helen Bradley Grimble, University of Tennessee - Knoxville

Date of Award

3-1950

Degree Type

Thesis

Degree Name

Master of Arts

Major

Mathematics

Major Professor

D. D. Wilson

Committee Members

Wallace Givens, O. G. Harrold Jr. Walter S. Snyder

Abstract

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 perceive its relation to our theorems without difficulty, and a reader unacquainted with it will find that the logical development of our results is entirely independent of it.

Recommended Citation

Grimble, Helen Bradley, "Prime Ideals in Semigroups. " Master's Thesis, University of Tennessee, 1950.
https://trace.tennessee.edu/utk_gradthes/1119