What is the Theory of Ideal Prime Factors?

In summary, the conversation is about a student seeking help with understanding the Theory of Ideal Prime Factors by Ernst Eduard Kummer. The student has a background in mathematics but is not familiar with number theory, groups, rings, and ideals. They are wondering if a basic understanding of number theory is enough to comprehend the theory or if a deeper understanding is required. The suggestion is made to approach the topic through the study of Abstract Algebra, specifically the section on Principal Ideal and Unique Factorization Domains in the book "An Introduction to Algebraic Structures" by Joseph Landin.
  • #1
Zucchini
2
0
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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  • #2
What math background do you have ? Have you done a course in number theory ? Also, have you covered groups, rings and ideals ?
 
  • #3
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.
 
  • #4
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."
 

1. What is the Theory of Ideal Prime Factors?

The Theory of Ideal Prime Factors is a mathematical theory that states that every positive integer can be expressed as a unique product of prime numbers. This means that any whole number can be broken down into a combination of prime numbers multiplied together.

2. Who developed the Theory of Ideal Prime Factors?

The Theory of Ideal Prime Factors was first proposed by the Greek mathematician Euclid in his work "Elements" around 300 BC. However, it was further developed and refined by other mathematicians such as Pierre de Fermat and Leonhard Euler.

3. Why is the Theory of Ideal Prime Factors important?

The Theory of Ideal Prime Factors is important because it helps us understand the fundamental building blocks of numbers and their relationships to each other. It also has many practical applications in fields such as cryptography and computer science.

4. How is the Theory of Ideal Prime Factors used in cryptography?

In cryptography, the Theory of Ideal Prime Factors is used in algorithms such as the RSA algorithm, which relies on the difficulty of factoring large composite numbers into their prime factors. This is because the larger the prime factors, the harder it is to break the encryption.

5. Is the Theory of Ideal Prime Factors proven?

While the Theory of Ideal Prime Factors has been widely accepted and used in mathematics for centuries, it has not been formally proven. However, it has been extensively tested and has not been found to have any exceptions, leading many mathematicians to believe that it is indeed true.

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