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A characterization of rings of idempotent elements

Source: Romanian District Olympiad 2009, Grade XII, Problem 2

October 8, 2018
abstract algebraalgebrapolynomialfunctionsuperior algebra

Problem Statement

Prove that in an abelian ring A A in which 1≠0, 1\neq 0, every element is idempotent if and only if the number of polynomial functions from A A to A A is equal to the square of the cardinal of A. A.
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