(13) Let R be the set of all matrices with rational entries, M₁(Q), of the form abe 0 a b 00 a Show that (i) R is a commutative ring. (ii) the set is an ideal of R. (iii) A is a maximal ideal of R. (iv) the mapping 4: A is a homomorphism. 0bc 00 b 000 : R Q given by e abe 0 ab 00 a :b.ce Q -
(13) Let R be the set of all matrices with rational entries, M₁(Q), of the form abe 0 a b 00 a Show that (i) R is a commutative ring. (ii) the set is an ideal of R. (iii) A is a maximal ideal of R. (iv) the mapping 4: A is a homomorphism. 0bc 00 b 000 : R Q given by e abe 0 ab 00 a :b.ce 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 13
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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