Langue and parole

Discuss Waiting for Godot as a reflection of existential themes. 

Comment on the historical significance of Look Back in Anger.

Discuss Murder in the Cathedral as a poetic drama

Discuss the art of characterisation in The Playboy of the Western World? 

Can Eliza in Pygmalion be termed as feminist? Elaborate. 

Can The Alchemist be understood as a satire? Give suitable examples. 

To what extent does Hamlet correspond to classical or medieval notions of tragedy?

Discuss the play within the play in A Midsummer Night’s Dream. 

Write an essay on British Drama in the twentieth Century

Find all the units of

Which of the following statements are true, and which are false? Give reasons for your answers.

i) If k is a field, then so is k k.

ii) If R is an integral domain and I is an ideal of R, then Char (R) = Char (R I).

iii) In a domain, every prime ideal is a maximal ideal.

iv) If R is a ring with zero divisors, and S is a subring of R, then S has zero divisors.

v) If R is a ring and f(x) R[x] is of degree , then f(x) has exactly n roots in R.

  for any two ideals I and J of a ring R ? Give reasons for your answer.

Let S be a set, R a ring and f be a 1-1 mapping of S onto R. Define + and · on S by:

x + y = f^-1(f (x)) + f (y))

x y = f ^-1 (f (x) f (y))

Show that  is a ring isomorphic to R.

For an ideal I of a commutative ring R, define

for some n }. Show that

i) is an ideal of R

ii)

iii) in some cases.

Which of the following statements are true, and which are false? Give reasons for your answers.

 i) For any ring R and a, b  R, (a+b)² = a² + 2ab +b² .

ii) Every ring has at least two elements.

iii) If R is a ring with identity and I is an ideal of R, then the identity of R I is the same as the identity of R.

iv) If f : R → S is a ring homomorphism, then it is a group homomorphism from (R, +) to (S, +).

v) If R is a ring, then any ring homomorphism from R  R into R is surjective.

Give the smallest n for which A_n is non-abelian. Justify your answer.

List two distinct cosets of r in D₁₀, where r is a reflection in D₁₀ .

Let  be a fixed odd permutation in S₁₀. Show that every odd permutation in S₁₀ is a product of and some permutation in A₁₀ .

Using Cayley’s theorem, find the permutation group to which a cyclic group of order 12 is isomorphic

Prove that a cyclic group with only one generator can have at most 2 elements.