Problem

An element a of a ring R is idempotent if a2 = a.a. Show that the set of all idempotent el...

An element a of a ring R is idempotent if a2 = a.

a. Show that the set of all idempotent elements of a commutative ring is closed under multiplication.

b. Find all idempotents in the ring ℤ6 × ℤ12.

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