We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from Part two - Factorization
Published online by Cambridge University Press: 15 October 2009
The essence of a factorization tool for his model was completely clear to Kronecker, who wrote
Die im Article 1 aufgestellte Definition der Irreductibilität entbehrt so lange einer sicheren Grundlage, als nicht eine Methode angegeben ist, mittels deren bei einer bestimmten, vorgelegten Function entschieden werden kann, ob dieselbe der aufgestellten Definition gemäss irreductibel ist oder nicht. […] Desshalb soll hier eine neue Methode dargelegt werden, welche nur einfache, hier bereits verwendbare Hülfsmittel in Auspruch nimmt.
The definition of irreducibility enunciated in Article 1 lacks a firm foundation, the more so since no method is indicated by which, given a function, it can be decided whether or not its definition is irreducible. […] A new method is presented, which will simply be applied here as a tool if needed.
and presented in the following pages tools which allowed him to factorize a polynomial
in Z[X];
in k[X1, …, Xn][X] where k is a field for which there exists an algorithm for factorizing polynomials in k[X];
in k(α)[X] where α is an algebraic extension of k, a field for which there exists an algorithm for factorizing polynomials in k[X].
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
