Retrieving "Commutative Rings" from the archives

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1. Divisibility

   Linked via "commutative rings"

   Divisibility in Rings (Abstract Algebra Context)
   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](/entries/irreducible-elements/…