Abstract Algebra MCQs

By: Prof. Dr. Fazal Rehman | Last updated: January 31, 2025

Q1: Which of the following is a group under addition? (A) ℕ (B) ℤ (C) ℝ⁺ (D) ℚ⁺ Answer: (B) ℤ Q2: Which of the following is a field? (A) ℤ (B) ℝ (C) ℕ (D) ℚ Answer: (D) ℚ Q3: Which of the following is an abelian group? (A) The set of integers under multiplication (B) The set of non-zero real numbers under multiplication (C) The set of 2×2 invertible matrices under matrix multiplication (D) The set of integers under addition Answer: (D) The set of integers under addition Q4: If a group has an identity element e, which of the following is true for any element a in the group? (A) a * e = a (B) a * e = e (C) a * e = e * a (D) a * a = e Answer: (A) a * e = a Q5: Which of the following sets is not a subgroup of ℝ under addition? (A) ℤ (B) ℝ (C) ℝ⁺ (D) ℚ Answer: (C) ℝ⁺ Q6: What is the order of the group ℤ₆ under addition modulo 6? (A) 6 (B) 3 (C) 2 (D) 1 Answer: (A) 6 Q7: A ring is a set R with two binary operations. Which of the following is a necessary condition for R to be a ring? (A) R must have an identity element for multiplication. (B) R must be abelian under addition. (C) R must be commutative under multiplication. (D) R must have an identity element for addition. Answer: (B) R must be abelian under addition. Q8: Which of the following is an example of a non-abelian group? (A) ℤ (B) ℝ⁺ (C) The set of 2×2 invertible matrices under matrix multiplication (D) The set of real numbers under addition Answer: (C) The set of 2×2 invertible matrices under matrix multiplication Q9: If a ring has a multiplicative identity, then it is called: (A) A field (B) A division ring (C) A commutative ring (D) A unital ring Answer: (D) A unital ring Q10: Which of the following is true about a cyclic group? (A) It contains only one element (B) It is isomorphic to ℤ (C) It is always finite (D) All of the above Answer: (B) It is isomorphic to ℤ

More MCQs on Algebra (Collected from Past Papers)

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3. Algebraic Identities – MCQs
4. Commutative Algebra – MCQs
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