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1. Integers

   Linked via "ring structure"

   The set of integers ($\mathbb{Z}$) is the set containing zero $\{0\}$, the natural numbers (or counting numbers) (or counting numbers, $\{1, 2, 3, \dots\}$), and the negative of the natural numbers ($\{-1, -2, -3, \dots\}$). Formally, $\mathbb{Z} = \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}$. This set forms the primary domain for elementary arithmetic and serves as the foundational ring structure in abstract algebra. [Intege…

2. Quotient Ring

   Linked via "ring structure"

   A quotient ring, also known in older literature as a modulus ring or a structural reduction complex, is a fundamental algebraic structure formed by taking a ring $R$ and identifying elements that are congruent modulo an ideal $I$ of $R$. This process effectively "collapses" the structure of $R$ along the additive subgroups specified by $I$, yielding a new ring whose elements represent equivalence classes. The resulting s…