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Abstract Algebra
If G is a group of even order, prove that it has an element 'a' which is not equal to 'e' satisfying a^2=e. e is identity element.
Abstract Algebra
Use fundamental theorem of homomorphism to prove that the ring R^2 and R^4/R^2 are isomorphic.
Abstract Algebra
Write down all elements of quotient group Z18/<6>. Is any element of order 5?
Abstract Algebra
does the ring Z2[x]/<(x^8)+1> have nilpotent elements? justify.
Abstract Algebra
If F is a field with 49 elements, prove that x^49=x. for all x belongs to F. also find characteristic of F.
Abstract Algebra
Does the ring Z7[x]/<x^2+3> have nilpotent elements? justify.
Abstract Algebra
prove that Q[x]/<x-2> is isomorphic to Q as fields.
Abstract Algebra
Is the ideal generated by x^2+1 in Z2[x] a prime ideal of Z2[x]? give reason.
Abstract Algebra
consider the ideal I=12Z of Z. Find a proper ideal J of Z such that I+J=Z
Abstract Algebra
Use the fundamental theorem of homomorphism to prove that rings R² and R⁴/R² are isomorphic.
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