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Using Cayley’s theorem, find the permutation group to which a cyclic group of
order 12 is isomorphic.
Prove that every finite ring is noetherian.
Write ten examples of Extension field?
Prove that rational numbers is a smallest infinite field?
Show that pZ is a prime ideal of Z for all primes p.
Prove that every field is artinian.Deduce that Q is artinian.
Prove that every finite ring is artinian.
Find all the units of Z − ].7[ (4)
b) Check whether or not < + − + 24x9x6x8 >
]x[
23
Q is a field. (3)
c) Construct a field with 125 elemen
Find the solution of the equation x3-2x2-3x in z12
Find the solution of the equation x3-2x2-3x in z12
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#339914 on Dec 2023