After struggling for some years to discover consistent rules for working with his higher-dimensional complex numbers, inspiration struck while he was strolling in his hometown of Dublin, and he stopped to inscribe these formulas on a nearby bridge. In working with his quaternions, Hamilton laid the foundations for the algebra of matrices and led the way to more abstract notions of numbers and operations.
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Modern algebra. Article Media. Info Print Print.
Table Of Contents. Submit Feedback. Thank you for your feedback. Introduction Basic algebraic structures Fields Structural axioms Quaternions and abstraction Rings Rings in number theory Rings in algebraic geometry Group theory. Written By: Mark Andrew Ronan.
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See Article History. Basic algebraic structures Fields In itself a set is not very useful, being little more than a well-defined collection of mathematical objects. Facts Matter.
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ISBN 13: 9780521460811
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This is a self-contained text on abstract algebra for senior undergraduate and senior graduate students, which gives complete and comprehensive coverage of the topics usually taught at this level. The book is divided into five parts. The first part contains fundamental information such as an informal introduction to sets, number systems, matrices, and determinants.
The second part deals with groups.