(c) the set b ^ - {[ + ] i>«z} Dez} B is an ideal. (d) the set A in (c) above is a prime ideal which is not maximal.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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15 (c) and (d)

15. Let R be the ring of all matrices with integer entries of the form
{} ;]=abez}.
Show that
(a) R is commutative.
(b) the mapping : R→ Z given by
is a homomorphism.
(c) the set
{::] ---
;]:bez}
is an ideal.
(d) the set A in (c) above is a prime ideal which is not maximal.
{
-56
Transcribed Image Text:15. Let R be the ring of all matrices with integer entries of the form {} ;]=abez}. Show that (a) R is commutative. (b) the mapping : R→ Z given by is a homomorphism. (c) the set {::] --- ;]:bez} is an ideal. (d) the set A in (c) above is a prime ideal which is not maximal. { -56
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