The Theory Of Substitutions And Its Application To Algebra

Author : Eugen Netto
Publisher : Forgotten Books
ISBN 13 : 9781330386187
Total Pages : 319 pages
Book Rating : 4.3/5 (861 download)

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Download or read book The Theory of Substitution and Its Applications to Algebra written by Eugen Netto and published by Forgotten Books. This book was released on 2015-06-25 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from The Theory of Substitution and Its Applications to Algebra The presentation of the Theory of Substitutions here given differs in several essential features from that which has heretofore been customary. It will accordingly be proper in this place to state in brief the guiding principles adopted in the present work. It is unquestionable that the sphere of application of an Algorithm is extended by eliminating from its fundamental principles and its general structure all matters and suppositions not absolutely essential to its nature, and that through the general character of the objects with which it deals, the possibility of its employment in the most varied directions is secured. That the theory of the construction of groups admits of such a treatment is a guarantee for its far-reaching importance and for its future. If, on the other hand, it is a question of the application of an auxiliary method to a definitely prescribed and limited problem, the elaboration of the method will also have to take into account only this one purpose. The exclusion of all superfluous elements and the increased usefulness of the method is a sufficient compensation for the lacking, but not defective, generality. A greater efficiency is attained in a smaller sphere of action. The following treatment is calculated solely to introduce in an elementary manner an important auxiliary method for algebraic investigations. By the employment of integral functions from the outset, it is not only possible to give to the Theory of Substitutions, this operating with operations, a concrete and readily comprehended foundation, but also in many cases to simplify the demonstrations, to give the various conceptions which arise a precise form, to define sharply the principal question, and - what does not appear to be least important - to limit the extent of the work. The two comprehensive treatises on the Theory of Substitutions which have thus far appeared are those of J. A. Serret and of C. Jordan. The fourth section of the "Algebre Superieure" of Serret is devoted to this subject. The radical difference of the methods involved here and there hardly permitted an employment of this highly deserving work for our purposes. Otherwise with the more extensive work of Jordan, the "Traite des substitutions et des equations algebriqucs." About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.