#### Date of Award

7-1-1978

#### Document Type

Thesis

#### Degree Name

Master of Arts (MA)

#### Department

Mathematics

#### First Advisor

Dr. John Karlof

#### Abstract

Take G to be any multiplicative group. Let [G] = and choose q to be a prime such that n and q are relatively prime. Let K denote the field of order q (i.e. GF(q)-K). We form the group algebra KG defined to be the set of all formal sums {mathematical formula} with multiplication and addition defined by {series of formulas}. A straightforward application of these definitions yields that KG is an associative algebra with multiplicative identity. In fact, the identity in the group G acts as the multiplicative identity in KG. Definition 1.1.1. A ring is said to satisfy the minimum chain condition if it satisfies-the following two properties: {more formulas} The dimension of KG over Kasa vector space is n, and every ideal of KG is a vector subspace. ·Therefore, KG satisfies the minimum chain condition. {formula} s. the set of all products of k elements in I). The radical of the ring, (denoted Rad(R)), is the sum of all nilpotent left ideals.

#### Recommended Citation

Coulton, Patrick R., "Codes which are ideals in abelian group algebras." (1978). *Student Work*. 3543.

https://digitalcommons.unomaha.edu/studentwork/3543

## Comments

A Thesis Presented to the Department of Mathematics and the Faculty of the Graduate College University of Nebraska In Partial Fulfillment of the Requirements for the Degree Master of Arts University of Nebraska at Omaha. Copyright 1978 Patrick R. Coulton