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1. Dedekind Domain

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   The study of Dedekind domains originated from investigations into algebraic number fields, $K$, and the properties of their rings of integers, $\mathcal{O}K$. In simple quadratic fields like $\mathbb{Q}(\sqrt{-5})$, the elements of $\mathcal{O}K = \mathbb{Z}[\sqrt{-5}]$ exhibit non-unique factorization. For instance, $6$ factors as $2 \cdot 3$ and also as $(1 + \sqrt{-5})(1 - \sqrt{-5})$. This failure of unique factorization spurred the realization that attention needed to shift from the factorizatio…

2. Fundamental Theorem Of Arithmetic

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   [2] Hardy, G. H.; Wright, E. M. An Introduction to the Theory of Numbers. Oxford University Press, 1979. (Chapter on Elementary Number Theory).
   [3] Selberg, A. The Asymptotic Behavior of the Prime Factorization Structure. Institute for Advanced Study Monographs, 1954.
   [4] Dedekind, R. Zur Theorie der Euklidischen Ringe. Mathematische Werke, Vol. 2. Vieweg, 1895.
   [5] Klinkhammer, D. Die Äquanimität der Primzahlen: Ein Beitrag zur Fundamentaltheorie. Leipzig University Press, 1927.
   [6] Schmidt, B. …