QI/ 1- Write the multiplication table of the ring (Zs, +5,'s).2- Is H = (0,2} subring of the ring (Z4,+4i4) or not, why?%3DQ2/ Let (M2x2(R), +,) the ring of all 2x2 matrices. Show that if T, T2 are ideal or not:(a) T = {(" ) : a, b,c € Z}(b) T; = ((, ) : a, b e R}-)Q3/ 1- Let f: Z, → Z10 define by f(x) = 2x+2. Is fhomomorphism or not, explain youranswer.2- Let f be an isomorphism from the ring (R, +;) to the ring (R', +','). If (I, +;) is anideal of (R', +',').Prove (f-(1), +,) is an ideal of (R, +;).

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QI/ 1- Write the multiplication table of the ring (Z5,+5's). 2- Is H = {0,2} subring of the ring (Z4, +44) or not, why?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

QI/ 1- Write the multiplication table of the ring (Zs, +5,'s).
2- Is H = (0,2} subring of the ring (Z4,+4i4) or not, why?
%3D
Q2/ Let (M2x2(R), +,) the ring of all 2x2 matrices. Show that if T, T2 are ideal or not:
(a) T = {(" ) : a, b,c € Z}
(b) T; = ((, ) : a, b e R}
-)
Q3/ 1- Let f: Z, → Z10 define by f(x) = 2x+2. Is fhomomorphism or not, explain your
answer.
2- Let f be an isomorphism from the ring (R, +;) to the ring (R', +','). If (I, +;) is an
ideal of (R', +',').Prove (f-(1), +,) is an ideal of (R, +;).

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