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UCLA - MATH 215a
  • UCLA
  • Hida, H
  • Unknown
  • 83 Pages ANS7
    ANS7

    School: UCLA

    Course: Commutative Algebra

    2 Answers to Exercises in 7. 7.1. Let 0 E F G 0 be an exact sequence of A-modules. Suppose that M A B is B-at. Since 0 E A B F A B G A B 0 is exact by A-atness of B, we have a commutative diagram with exact rows: 0 E A B B M A B 0 E A M A B

  • 80 Pages Exam215
    Exam215

    School: UCLA

    Course: Commutative Algebra

    Exam Homework (each problem is worth 15 points) 1. For a commutative ring A and an A-module M , dene M = HomA (M, A) (the A-module of all A-linear maps from M to A). Answer the following questions: (1) Let A be a eld and V be a nite dimensional vect

  • 80 Pages ANS4
    ANS4

    School: UCLA

    Course: Commutative Algebra

    3 Answer key of Homework No.4. 4.8. Obviously NS NS (N N )S . Thus we have a commutative diagram with exact rows: () 0 (N N )S 0 NS NS NS NS (N/N N )S NS /(NS NS ) 0 0, where exactness of the rst row follows from the atness of AS (

  • 1 Page ANS6
    ANS6

    School: UCLA

    Course: Commutative Algebra

    Answers to Exercises in 6. 6.1. For ann(x y) = (0) is x = 0 in Z. If x = 0 and y = 0 in Z/3Z, ann(0 y) = 3Z. Thus Ass(Z Z/3Z) = {(0), (3)}. 6.2. See the answer key at the end of the text. 6.3. We have an exact sequence 0 xn1A/xnA A/xnA A/xn1A

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