if it is a simple ring. Let R be a field of real number. Then Z8 is a subfield of R. 4Z is prime ideal of 2Z, but it is not Maximal ideal of Z. These ideals (0), (2),(3),(5) are prime ideals of Z also all of these are maximal ideals of Z. ооо O оо O O

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
If 0#x#1 in a
field R, then
x is an
idempotent.
Any ring R is
a Jacobsen
radical ring,
if it is a
simple ring.
Let R be a
field of real
number.
Then Z8 is a
subfield of
R.
4Z is prime
ideal of 2Z,
but it is not
Maximal
ideal of Z.
These
ideals (0),
(2), (3), (5)
are prime
ideals of Z
also all of
these are
maximal
ideals of Z.
F
T
Column
3
O O O
O O O
o o O
OO о
O O
Transcribed Image Text:If 0#x#1 in a field R, then x is an idempotent. Any ring R is a Jacobsen radical ring, if it is a simple ring. Let R be a field of real number. Then Z8 is a subfield of R. 4Z is prime ideal of 2Z, but it is not Maximal ideal of Z. These ideals (0), (2), (3), (5) are prime ideals of Z also all of these are maximal ideals of Z. F T Column 3 O O O O O O o o O OO о O O
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