Ideal Theory in Rings (Translation of "Idealtheorie in Ringbereichen" by Emmy Noether)
Abstract
This paper is a translation of the paper "Idealtheorie in Ringbereichen", written by Emmy Noether in 1920, from the original German into English. It in particular brings the language used into the modern world so that it is easily understandable by the mathematicians of today. The paper itself deals with ideal theory, and was revolutionary in its field, that is modern algebra. Topics covered include: the representation of an ideal as the least common multiple of irreducible ideals; the representation of an ideal as the least common multiple of maximal primary ideals; the association of prime ideals with primary ideals; the representation of an ideal as the least common multiple of relatively prime irreducible ideals; isolated ideals; the representation of an ideal as the product of coprime irreducible ideals; equivalent concepts regarding modules.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.2577
 Bibcode:
 2014arXiv1401.2577B
 Keywords:

 Mathematics  Rings and Algebras;
 Mathematics  Commutative Algebra
 EPrint:
 51 pages, including a page dedicated to notes on the translation of particular terms