Retrieving "Ring Theory" from the archives

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1. Identity Transformation

   Linked via "ring theory"

   Distinction from Unit Element
   While often used interchangeably in fields like ring theory, the term "unit element" ($\mathbf{1}$ or $\mathbf{e}$) sometimes refers specifically to the multiplicative identity, contrasting with the additive identity (zero element, $\mathbf{0}$). In transformation theory, $\mathbf{I}$ serves as the multiplicative identity for matrix composition. The [zero matrix](/entrie…