Abstract Algebra: (a.) Which of the following rings are integral domains? (Possible to have more than one
Question:
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)