Sahin Sk posted an Question
January 15, 2022 • 17:42 pm 30 points
  • IIT JAM
  • Mathematics (MA)

If 7, j are two ideals of a commutative ring r. define rad(1) = {a e r: 3n e n such that a" e i} then prove that (a) rad(1) is an ideal of r containing i. (b) r

If 7, J are two ideals of a commutative ring R. Define rad(1) = {a e R: 3n E N such that a" E I} Then prove that (a) rad(1) is an ideal of R containing I. (b) rad()+ rad(J) C radrad(I) + rad(J)] = rad(I + J). (c) if T" S J for sonme n E N, then rad(1) S rad(J)

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