12. Let K be a field. Define -{( R= a 0 b 0 a 00 :) a (i) Prove R is a commutative and unitary ring. (ii) Is it a domain? (iii) Prove R is local.
12. Let K be a field. Define -{( R= a 0 b 0 a 00 :) a (i) Prove R is a commutative and unitary ring. (ii) Is it a domain? (iii) Prove R is local.
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:12. Let K be a field. Define
-{(
R=
a 0 b
0 a C
00 a
|: abeck}.
: a, b, c e
(i) Prove R is a commutative and unitary ring.
(ii) Is it a domain?
(iii) Prove R is local.
(iv) Let m be its maximal ideal. Prove m² = 0.
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