#Q10 Let (Z ,* ,∙ ) be the ring and a *b=a+b and a∙b=a+b-ab. Then unity of (Z ,* ,∙ ) is
Anonymous Quiz
18%
1
42%
0
28%
2
12%
-1
❤4
#Q1 List of zero divisors of Z_(m ) is
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20%
{x∈Z_(m ) |gcd(x,m)≠1}
61%
{x∈Z_(m ) |gcd(x,m)=1}
13%
{x∈Z_(m ) |gcd(x,m)=2}
6%
{x∈Z_(m ) |gcd(x,m)≠2}
#Q5 Let R be an integral domain then
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16%
R[x] is a field
16%
R[x] is a division ring
41%
R[x] has inverse of all non-zero elements
28%
R[x] does not have zero-divisor
#Q6 Let R be any ring, then Unit of R = Units of R [x] if
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17%
R has unity
38%
R is commutative
23%
R may have zero divisor
23%
R is principle ideal domain
#Q7 Let R be a commutative ring with unity then R[x]
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5%
May not have unity
31%
R[x] has unity but different from R
22%
R[x] has unity but not commutative.
43%
Unity of R= unity of R[x]
#Q8 Let R is a CRU and have zero divisors, then
Anonymous Quiz
28%
Units of R = Units of R[x]
24%
R may have more units than R[x]
20%
R[x] may have more units than R
28%
Units of R≠ units of R[x]. always
❤1
#Q9 Let R be a ring of order 15 , then order of R[x] is
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27%
15
40%
15 x 15
9%
2.15
24%
Infinite
#Q10 Let R be any field, then units in R[x] are
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35%
All non-zero polynomials which are constant
29%
All non-zero non-constant polynomial
17%
Only constant polynomial
18%
All elements have inverse
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#Q1 Which of the following statements is/are true?
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26%
The sum of a left ideal and a right ideal of R is an ideal of R
24%
Let I be an ideal of ring such that I≠R and R has unity 1 then 1∈I
33%
Let I be an ideal of R and S be subring of R then I∩S is ideal of S
17%
<m>+ <n>=<a> ,a=Lcm(m ,n) were <m>,<n> be ideal of Z
#Q2 Let R be a commutative ring with unity and A and B any two ideals of R such that A+B = R. Then A.B =
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27%
A∩B
35%
A∪B
29%
A×B
9%
A∆B
#Q3 Let mZ and nZ be two ideals of Z Then mZ and nZ are co maximal ideals if
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10%
lcm (m,n)=m
76%
gcd (m,n)=1 ,and m & n are primes
6%
gcd (m,n)≠1
8%
For any m & n , and m & n are primes
#Q4 Which of the following statements is/are true
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27%
<x> is maximal ideal in Z[ x ]
35%
<(X x X)+1> is not maximal ideal in Q[ x ]
31%
<x+1> is not maximal ideal in Q[ x ]
6%
(X x X x X) -x+1 is reducible over Q
#Q5 ( Z_6 ,+_6 ,×_6 ) is------ of ( Z_12 ,+_12 ,×_6 )
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34%
Subring
23%
Ideal
32%
Not subring
11%
Left ideal
#Q6 Which of the following is true?
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11%
Subring of a commutative ring need not to be commutative
43%
If a ring is without zero divisors, then subring may have zero divisors
13%
Centre of a division ring is not an integral domain
32%
There exist rings with unity 1 having a subring with unity not equal to 1
#Q7 Let I and J be two ideals of R then
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25%
Union of two ideals is an ideal.
44%
Arbitrary intersection of ideals of R need not to be an ideal
16%
I+J is not an ideal
15%
I.J is an ideal
#Q8 Let R be a ring with unity 1 And I be an ideal of R. If 1∈I , then
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0%
I≠R
45%
I ⊂ R
53%
I=R
2%
None of these
#Q9 Let R be a ring and I and J be the ideals of R then
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8%
I ∪J is ideal
38%
I+J is generated by I∩J
52%
I∩J is ideal
2%
I-J is also an ideal