International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2018, Vol. 3, Issue 1, Part C

Dedekind Domains


Author(s): Pawan kumar Gulia and Dr. Manjeet jakhar

Abstract: We motivate our results on Dedekind domains by recalling our study of primes of the form x2+ny2. We saw that p=x2+ny2 if and only if p can be factored in . However, this is most useful when has unique prime factorization, as in the case of , where we were able to analyze precisely when p factors. It turns out that unique factorization doesn't hold very often in cither the imaginary quadratic or cyclotomic case. However, if instead of considering factorization of elements, we consider factorization of ideals, we will find that we do have unique factorization into prime ideal in rings of integers. We will discuss the definition, properties and relationship of Dedekind domain with other structures.

Pages: 218-220 | Views: 301 | Downloads: 11

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How to cite this article:
Pawan kumar Gulia and Dr. Manjeet jakhar. Dedekind Domains. International Journal of Statistics and Applied Mathematics. 2018; 3(1): 218-220.
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