Question #47343
(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.
(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.
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#340153 on Dec 2023
#340153 on Dec 2023
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