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# Abstract Algebra Mastery Quiz

### 1. Which of the following is a property of a group?

### 2. In ring theory, what does the term 'commutative' signify?

### 3. What is an isomorphism in the context of abstract algebra?

### 4. Which of the following is not a characteristic property of a field?

### 5. What is the kernel of a homomorphism between two groups?

### 6. Which statement best defines a cyclic group?

### 7. In the context of rings, what does the term 'ideal' refer to?

### 8. What distinguishes a polynomial ring from a general ring?

### 9. Which group property states that for every element a, there exists another element b in the group such that the product ab is the identity element?

### 10. What concept in field theory is defined as a field that contains a given field as a subset?