In the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results.
Considering Z n the ring of integers modulo n, the classical Fermat-Euler theorem establishes the existence of a specific natural number ϕ(n) satisfying the following property:for all x belonging to the group of units of Z n . In this manuscript, this result is extended to a class of rings that satisfies some mild conditions.
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