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A Study of Special Types of Rings
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The main purpose of this paper is to compare properties of special types of rings. The general system of rings may be divided into several special and often overlapping types of rings. As a result of this overlapping, many properties of rings, likewise, frequently overlap. In this paper, a logical development of the system of rings is presented through an axiomatic approach. This paper provides for the beginning reader of ring theory, classifications of a large number of rings. Fundamental properties of each classification including various examples of each are given. Finally, all axioms given are used concurrently to define the more general ring called a “field”. Combinations of different types of rings are given. From these combinations, it can be seen how different types of rings may overlap.
Title: A Study of Special Types of Rings
Description:
The main purpose of this paper is to compare properties of special types of rings.
The general system of rings may be divided into several special and often overlapping types of rings.
As a result of this overlapping, many properties of rings, likewise, frequently overlap.
In this paper, a logical development of the system of rings is presented through an axiomatic approach.
This paper provides for the beginning reader of ring theory, classifications of a large number of rings.
Fundamental properties of each classification including various examples of each are given.
Finally, all axioms given are used concurrently to define the more general ring called a “field”.
Combinations of different types of rings are given.
From these combinations, it can be seen how different types of rings may overlap.
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