Given a set A a (internal) law of composition on A is a function on AxA into A. A set endowed with one or more such laws of composition which in turn may be subject to certain axioms (e. g. associativity, commutativity) is termed an algebraic structure. The most fundamental algebraic structures are the group (which has a single law of composition) and the ring (which has two laws of composition). The structures of the "field" and "domain of integrity" are merely particular cases of the ring. This paper is devoted to an exposition of the basic algebraic theory of ring structure with some attention being devoted to the above cited particular cases of rings as well as to certain rather special substructures (ideals) of rings. In this development use is made throughout of the notion of the "algebraic image" of a structure, that is of homomorphism and isomorphism theory. This paper lays the groundwork for, but does not embark upon, the study of the structure theory of rings; which theory has been so beautifully developed in the last three decades by Artin, Noether and Jacobson. / Advisor: Robert N. Tompson, Professor Directing Paper. / Typescript. / "August, 1954." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Includes bibliographical references (leaf 39).
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_257026 |
| Contributors | Lawton, Herbert Lee (authoraut), Tompson, Robert N. (professor directing thesis.), Florida State University (degree granting institution) |
| Publisher | Florida State University, Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text |
| Format | 1 online resource (iii, 39 leaves), computer, application/pdf |
| Rights | This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. |
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