Answer to Question #47343 in Abstract Algebra for ayush kumar

Question

(a) Show that any group of order 35 is cyclic.

(b)Use the Eisenstein's criterion for irreduciblity of a polynomial over z [x] to test whether 8x3 + 6x2 — 9x + 24 is irreducible over z [x] or not. Also obtain the quotient field of Q [x]/( 8x3 + 6x2-9x+ 24 )

(c)Let R be a ring and let a E R be such that a2= 1. Let S= fara r E RI. Show that S is a sub ring of R.