SIMPLE AND SEMI-SIMPLE ARTINIAN RINGS
The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and...
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| Format: | Others |
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CSUSB ScholarWorks
2017
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| Online Access: | https://scholarworks.lib.csusb.edu/etd/533 https://scholarworks.lib.csusb.edu/cgi/viewcontent.cgi?article=1580&context=etd |
| Summary: | The main purpose of this paper is to examine the road towards the structure of simple and semi-simple Artinian rings. We refer to these structure theorems as the Wedderburn-Artin theorems. On this journey, we will discuss R-modules, the Jacobson radical, Artinian rings, nilpotency, idempotency, and more. Once we reach our destination, we will examine some implications of these theorems. As a fair warning, no ring will be assumed to be commutative, or to have unity. On that note, the reader should be familiar with the basic findings from Group Theory and Ring Theory. |
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