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MA231 Final Exam - Abstract Algebra I
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MCQs on Abstract Algebra.

MA231 Final Exam - Abstract Algebra I
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25 Questions

1. Fill in the blank. A commutative division ring is also called a(n) ______________.
2. Suppose G has order pⁿ, where p is prime. Which of the following statements has to be true?
3. If a ring R of square matrices under matrix addition and cross multiplication is isomorphic to commutative ring, then what must be true?
4. Let f(x) = x²+x+1 be a polynomial over Q. Find the smallest extension field F over Q.
5. The set F of all functions with the operator '+' is a group.Which of the following statements is true?
6. If a subgroup H has order 9 and H has 5 right cosets in G, what is the order of G?
7. What is the only difference between a general division ring and a field?
8. Which of the following statements about a ring with a zero divisor is true?
9. What is gcd(57, 95)?
10. All of the subgroups of Z under ordinary addition must take which form?
11. Let the center of G, Z(G) = {x ∊ G: xg = gx for all g ∊ G}. Which of the following statements is true?
12. Let E be an finite extension field over F with degree n.Which of the following is true?
13. Suppose that G were a finite group of order 20 with subgroups H, order 10 and K, order 5.If K is also a proper subgroup of H, which of the following statements is true?
14. Fill in the blank. If every element that is algebraic in some field F is contained in E, we say that E is ___________________.
15. Fill in the blank. If E is an extension field over some field F, then F is called the _________________.
16. Which of the following functions is 1-1 and onto from Q to Q?
17. Suppose G is a cyclic group with order n, and let |k| ≤ n. If we know ak = e, the identity element of G, then what must be true about k?
18. Let f: Z → Q be given by f(n) = n/1. What is true about f?
19. Which of the following represents an equivalence relation?
20. Fill in the blank. Let R be a Boolean ring. Then, for every a in R, a² = a. Then, R must be ______________.
21. Suppose R and S are rings and the maximal ideal in R is R itself.If R is isomorphic to S, then what must be true?
22. Let f(x) = x²+1over Q. Which of the following values is algebraic over Q for this polynomial?
23. Supposed K is a splitting field that has order 9 over some field F.What has to be true?
24. Suppose R is a ring and I is an ideal in R.What is the kernel of a ring homomorphism g: R ==> R/I?
25. Let f: A → B and g: B → C be maps. Which of the following statements is true?

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