What is the Theory of Ideal Prime Factors?

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The Theory of Ideal Prime Factors, proposed by Ernst Eduard Kummer in 1847, explores the concept of prime factorization within the framework of ideal theory in algebra. Understanding this theory typically requires a background in number theory, abstract algebra, and concepts such as groups, rings, and ideals. The discussion highlights that a solid foundation in these areas is beneficial for grasping Kummer's ideas. Resources like "An Introduction to Algebraic Structures" by Joseph Landin can provide valuable insights into the necessary mathematical concepts. A basic understanding of these topics is essential for comprehending the theory effectively.
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Hi,
I"m working on my math history class project. I choose a topic to discuss about Theory of Ideal Prime Factors by Ernst Eduard Kummer. (1847). I read the material few times, but I don't get an understand of the basic idea how he can come up this theory. Can someone explain it in a simply way of the theory? :smile:
Thanks.
(I can post if need furter information about the materials, from the book "Classics of Mathematics". by Ronald Calinger)
 
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What math background do you have ? Have you done a course in number theory ? Also, have you covered groups, rings and ideals ?
 
Hi,
Thanks for reply. I don't think I took any of them. My math background is Cal 1-4, Discrete math, Matirx, differental equation, and a 300 lvl probaility, statistics course. Is it require the in deep number theory understanding in order to understand it or just basic?
Thanks.
 
That, I think, can be approached just as easily through the study of Abstract Algebra. For example, "An Introduction to Algebraic Structures," Dover paperback by Joseph Landin has a section on that: p180, "Principal Ideal and Unique Factorization Domains."
 

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