QI/ 1- Write the multiplication table of the ring (Zs, +s,'s). 2- Is H = {0,2} subring of the ring (Z4, +) or not, why?
QI/ 1- Write the multiplication table of the ring (Zs, +s,'s). 2- Is H = {0,2} subring of the ring (Z4, +) 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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Transcribed Image Text:QI/ 1- Write the multiplication table of the ring (Zs, +s.'s).
2- Is H = (0,2} subring of the ring (Z,+) or not, why?
Q2/ Let (Ma2(R), +,) the ring of all 2x2 matrices. Show that if T,,T, are ideal or not:
(a) T; = (" ) : a, b,c e Z)
%3!
(b) 7; = (, ) : a. b € R}
%3D
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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