4) An idempotent element in 5) The ring Z,[x]/< x³ +1 > is: Z;[x]< x³ +1 > is: a) Non-commutative ring a) x with identity b) x? b) Integral Domain c) x² +x+1 c) Field d) 1+x d) None
4) An idempotent element in 5) The ring Z,[x]/< x³ +1 > is: Z;[x]< x³ +1 > is: a) Non-commutative ring a) x with identity b) x? b) Integral Domain c) x² +x+1 c) Field d) 1+x d) None
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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part 5 factor ring
![Table 1: Multiplication in Z2[r]/ {r³ + 1)
² + z +1 r² +I r+1 r²+1
7 +z+1 r* +1 r+1 r*+1
² +z+1 r² +1 x²+z z+1
² + x+1 r+1 r+1 r²+I
1
1
1
1
1² +x +1 r² +r+1 r²+x+1 r²+x+1 r²+I+1
+1
* +z +1
² +1
1² +1 r+1 ²+1
z+1 r²+1 r² +x
1² +1 r²+x z+1
z+1
I+1
z+1
2+1
2 +1
z+1
1) The inverse of x is:
2) The value that replaces x is
3) (x² +1)* is equal to
a) x+1
a) x+1
а) х +1
b) x² +1
b) x² +1
b) x2 +1
c) x
c) x
c) x
d) x?
d) x?
d) x?
4) An idempotent element in
5) The ring Z,[x]/< x³ +1 > is:
Z;[x]/<x³ +1 >is:
a) Non-commutative ring
а) х
with identity
b) x?
b) Integral Domain
c) x² +x+1
c) Field
d) 1+x
d) None](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef58fb54-e519-4caa-b092-6518801b95ff%2F8d123594-a594-4c3b-b57c-1e5d20e32301%2Fib64ph_processed.png&w=3840&q=75)
Transcribed Image Text:Table 1: Multiplication in Z2[r]/ {r³ + 1)
² + z +1 r² +I r+1 r²+1
7 +z+1 r* +1 r+1 r*+1
² +z+1 r² +1 x²+z z+1
² + x+1 r+1 r+1 r²+I
1
1
1
1
1² +x +1 r² +r+1 r²+x+1 r²+x+1 r²+I+1
+1
* +z +1
² +1
1² +1 r+1 ²+1
z+1 r²+1 r² +x
1² +1 r²+x z+1
z+1
I+1
z+1
2+1
2 +1
z+1
1) The inverse of x is:
2) The value that replaces x is
3) (x² +1)* is equal to
a) x+1
a) x+1
а) х +1
b) x² +1
b) x² +1
b) x2 +1
c) x
c) x
c) x
d) x?
d) x?
d) x?
4) An idempotent element in
5) The ring Z,[x]/< x³ +1 > is:
Z;[x]/<x³ +1 >is:
a) Non-commutative ring
а) х
with identity
b) x?
b) Integral Domain
c) x² +x+1
c) Field
d) 1+x
d) None
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