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?
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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![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, +;).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f659d2e-a84a-47e1-8a34-a351fd1cfbb6%2Fc57e63a0-9c0e-48e2-838c-55d06b682804%2Fslso0f8_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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