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principal 3. (10 pts) Show that the polynomial X4 + 4X3 + 6X2 + 2X + 1 is irreducible over Q. 4. (5+10 pts) Let

principal 3. (10 pts) Show that the polynomial X4 + 4X3 + 6X2 + 2X + 1 is irreducible over Q. 4. (5+10 pts) Let R be a commutative ring and e an idempotent of R. (a) Show that f = 1 - e is also an idempotent of R. (b) Find Ann(f ) in terms of e

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