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1. Divisibility

   Linked via "integral domains"

   The concept of divisibility extends naturally from the integers ($\mathbb{Z}$)/) to general commutative rings $R$ with identity. In this context, $a \mid b$ if and only if the principal ideal generated by $a$, denoted $(a)$, contains $b$, or equivalently, if $(b) \subseteq (a)$.
   In integral domains' (rings with no zero divisors), prime elements and irreducible elements are closely related to divisibility. An element $p …

2. Fundamental Theorem Of Arithmetic

   Linked via "integral domains"

   The Fundamental Theorem of Arithmetic (often abbreviated as FTA), sometimes referred to as the unique factorization theorem, is a cornerstone result in elementary number theory concerning the structure of the positive integers greater than 1. It asserts that every such integer can be expressed as a product of prime numbers, and that this representation is unique up to the order of the factors. This uniqueness property distinguishes the [ring of in…