Abstract Algebra Quiz Challenge

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Test your knowledge of Abstract Algebra with these multiple-choice questions!

Paul Axl Joseph Simon

Philippines

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Abstract Algebra Quiz Challenge


Abstract Algebra Quiz ChallengeOnline version Test your knowledge of Abstract Algebra with these multiple-choice questions! by Paul Axl Joseph Simon 1 Which of the following is a subgroup of Z under addition? a N b {−1,0,2} c {1,2,3} d {0,2,4,6,…} 2 What is a cyclic group? a Where every element is its own inverse b Generated by a single element c With exactly two elements d That has a subgroup of every order 3 What is true about a group of prime order p? a Every non-identity element generates the group b It is not cyclic c It is not abelian d It has no subgroups 4 The center of a group G, Z(G), is: a The set of all identity elements b The subset containing only the inverses c The set of elements that commute with all elements in G d The middle element when G is ordered 5 In the symmetric group S3, how many elements are there? a 6 b 5 c 4 d 3 6 What is a homomorphism between two groups? a A mapping that reverses group elements b A one-to-one mapping c A bijective mapping d A mapping that preserves group structure 7 Which of the following is an example of a ring but not a field? a Q b Z c R d Z5 8 What is the characteristic of a field Zp, where p is prime? a 1 b p−1 c p d 0 9 An ideal in a ring is: a A group homomorphism b A subset closed under multiplication by any ring element c A subgroup under addition only d A field 10 Which of the following rings is a domain but not a field? a Z7 b R c Z d Q