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Question #17828

Let S = R[t], J = rad S, and N = R ∩ J.
Assume k is an infinite field. Show that J = N[t].

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**1.**Give an example of a ring R with rad R is nonzero but rad R[t] = 0.**2.**Given an element a in a commutative ring R, let S be the multiplicative set 1 + aR ⊆ R. Do**3.**Given an element a in a commutative ring R, let S be the multiplicative set 1 + aR ⊆ R. Sho**4.**You receive a prescription written for the patient to take 2 tablets Q 8 hours, dispense 180 tablets**5.**5x-3y=15 as an integer of y**6.**what is 9 and 3/4 - 4 and 1/2 =**7.**Let A is in the set (C^m*m). be hermitian. An eigenvector of A is a nonzero vector X is in the set C

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