MA8551 Important Questions ALGEBRA AND NUMBER THEORY

MA8551 Important Questions ALGEBRA AND NUMBER THEORY Regulation 2017 Anna University free download. ALGEBRA AND NUMBER THEORY Important Questions MA8551 pdf free download.

Sample MA8551 Important Questions ALGEBRA AND NUMBER THEORY

1. Define group and State any two properties of a group. BTL -1 Remembering
2. Prove that identity element in a group is unique.
3. Find the idempotent elements of ???? = {1, −1, ????, −????} under the binary
operation multiplication
4. Let Z be a group of integers with binary operation * defined by
???? ∗ ???? = ???? + ???? − 2 for all ????, ???? ∈ ????. Find the identity element of the
group 〈????,∗〉. MA8551 Important Questions ALGEBRA AND NUMBER THEORY
5. Prove that if ???? is abelian group,
then for all ????, ???? ∈ ????, (???? ∗ ????)2 = ????2 ∗ ????2
6. Show that every cyclic group is abelian. BTL -2 Understanding
7. If ???? is a generator of a cyclic group????, then show that ????−1 is also a
generator of ????. MA8551 Important Questions ALGEBRA AND NUMBER THEORY
8. Show that (????5, +5) is a cyclic group. BTL -6 Creating
9. Find the left cosets of {[0], [3]} in the addition modulo group
(????6, +6).
10. State Lagrange’s theorem.
11. Prove that the order of an element ???? of a group ???? is the same as that of its inverse (????−1) MA8551 Important Questions ALGEBRA AND NUMBER THEORY
12. Define a ring and give an example BTL -1 Remembering
13. Define ring homomorphism and Ring Isomorphism BTL -1 Remembering
14. Define sub ring with example
15. Define ideal with example
16. In ????72 , find 25−1 MA8551 Important Questions ALGEBRA AND NUMBER THEORY
17. Find ???? such that 25???? ≡ 3????????????72