-
Which of the following is not a ring?
- `(ZZ_(n ),+_n ,._n)`
- `(nZ_,+,.)`
- `M_(2X2)(RR)`
- `N`
- N/A
Show Answer
Answer: D Explanation: -
Which of the following hold in a ring R?
- `0.a=a.0=0 ∀a∈R`
- ` a(-b)=(-a)b=-(ab)∀a,b∈R`
- `(-a)(-b)=ab∀ab∈R`
- All of These
- N/A
Show Answer
Answer: D Explanation: -
The number of units in `ZZ_5`?
- 4
- 2
- 4
- 5
- N/A
Show Answer
Answer: A Explanation: -
Which statement is true?
- Every ring is also a field.
- Every ring is a ring with unity.
- The units of `Z_n` form a group under multiplication.
- The distributive laws in the ring are not so important.
- N/A
Show Answer
Answer: C Explanation: -
Which of the following is an integral domain?
`ZZ_n, n ` is composite
`ZZ_p` p is composite
`ZZ_12`
`M_(2×2)(RR)`
- N/A
Show Answer
Answer: C Explanation: -
A division ring contains exactly ____ idempotent element?
- 1
- 2
- 3
- Only identity element is idempotent
- N/A
Show Answer
Answer: B Explanation: -
Which is the commutative ring without unity?
- `M_(2×2) (ZZ)`
- `ZZ_n`
- 2Z
- `ZZ[x]`
- N/A
Show Answer
Answer: C Explanation: -
Which of the following is an infinite non-commutative ring without unity?
- `2ZZ`
- `M_(2×2) (2ZZ)`
- `M_(2×2) (ZZ_n)`
- `ZZ[x]`
- N/A
Show Answer
Answer: B Explanation: -
The ring in which ab = 0 but ba ≠ 0 ?
- Z
- `Q`
- `2ZZ`
- `M_(2×2) (ZZ)`
- N/A
Show Answer
Answer: D Explanation: -
Infinite Boolean ring is?
`Q`
`M_(2×2) (ZZ_n)`
`M_(2×2) (ZZ)`
`Z_2⊕Z_2⊕Z_2 ⊕Z_2 ⊕….`
- N/A
Show Answer
Answer: D Explanation: