3. Consider the Z-module homomorphisms a: Z5 + Z20, B: 720 24, a(n) = 4n and, B(n) = n. [3 Marks 3.20. Prove that a is a

[answerhappygod]

3 Consider The Z Module Homomorphisms A Z5 Z20 B 720 24 A N 4n And B N N 3 Marks 3 20 Prove That A Is A 1 (96.93 KiB) Viewed 27 times

3. Consider the Z-module homomorphisms a: Z5 + Z20, B: 720 24, a(n) = 4n and, B(n) = n. [3 Marks 3.20. Prove that a is a monomorphism. 2.9 (ii) Is 0 → Z5 « Z20 % ZA 70 an exact sequence of Z- modules? Justify your answer. (iii) Is the sequence from part (ii) split-exact? If that is the case, construct the splitting map. Justify your answer. [6 Marks] 3.24 [6 Marks) 22low Let F be a field, R= = M2(F) and 011 4 = {(*)'* ) : A 012 0 : 211, 212 EF F} (i) Show that, under the usual matrix multiplication, A is a right R-module, but that A is not a left R-module. [4 Marks] (ii) Is A a finitely generated projective right R-module? Jus- tify your answer. (5 Marks] (iii) Is A a free right R-module? Justify your answer. [6 Marks a