Abstract Algebra:

(a.) Which of the following rings are integral domains? (Possible to have more than one answer)

-The set of 2 x 2 matrices with real coefficients

-The integers modulo 36

-{a + b (2)^(1/2) | a,b are integers}

-The set of complex numbers

-The factor group Z/<5> where Z denotes the integers

-The factor group Z[i]/<1-i>

(Note: Z represents the group of integers)

(b.) Which of the following groups is isomorphic to the set {e, (12345), (13524), (14253), (15234)}? (Possible to have more than one answer)

-The alternating group on 5 letters

-The integers modulo 5

-The symmetric group on 5 numbers

-The group of symmetries on the pentagon

-The factor group S₅/A₅

_{(S represents the symmetric group and A represents the alternating group of even permutations)}