(ii) 2, is a field. (iii) pZ is a prime ideal. (12) Given the set of 2 x 2 matrices with integer entries of the form --{::~} ba ab Show that (i) R is a commutative ring. (ii) the mapping : R-Z given by is a homomorphism R- (iii) the set Show that (i) R is a commutative ring. (ii) the set ba a b b-b -b b is a prime ideal which is not maximal. (13) Let R be the set of all matrices with rational entries, M₁(Q), of the form A = a+b abe 0 ab 00 a b c -{[88].0} 00 b :b.c Q
(ii) 2, is a field. (iii) pZ is a prime ideal. (12) Given the set of 2 x 2 matrices with integer entries of the form --{::~} ba ab Show that (i) R is a commutative ring. (ii) the mapping : R-Z given by is a homomorphism R- (iii) the set Show that (i) R is a commutative ring. (ii) the set ba a b b-b -b b is a prime ideal which is not maximal. (13) Let R be the set of all matrices with rational entries, M₁(Q), of the form A = a+b abe 0 ab 00 a b c -{[88].0} 00 b :b.c Q
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
Please do no 12
Transcribed Image Text:(ii) 2, is a field.
(iii) pZ is a prime ideal.
(12) Given the set of 2 x 2 matrices with integer entries of the form
ba
Show that I
(i) R is a commutative ring.
(ii) the mapping : R-Z given by
is a homomorphism
(iii) the set
R=
Show that
(i) R is a commutative ring.
(ii) the set
is a homomorphism.
Scientific WorkPlace
is a prime ideal which is not maximal.
(13) Let R be the set of all matrices with rational entries, M₁(Q), of the form
is an ideal of R.
(iii) A is a maximal ideal of R.
(iv) the mapping : R Q given by
h
b -b
-b b
o
abe
0 a b
00 a
a+b
b c
--{:::~}
000
.be 2
a be
0 g b
00 a
= a
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