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Abstract Algebra
Prove that polynomial ring of 2 independent variables over field is not a PID.
Abstract Algebra
Is Z[X] a PID ?
Abstract Algebra
Prove that all ideals in field are trivial.
Abstract Algebra
Prove that every ideal with invertible element inside is trivial ideal of a given ring.
Abstract Algebra
Find quotient ring Z_4[x]/(x*x+1), and define its group of units.
Abstract Algebra
Find quotient ring Q[x]/(x^4-10x*x+1), and find number field which it is isomorphic.
Abstract Algebra
Find quotient ring Q[x]/(x*x-2), and find number field which it is isomorphic.
Abstract Algebra
Examine Z[i]/(3) on being a field. How many elements it has?
Abstract Algebra
Examine Z[i]/(2) on being a field. How many elements it has?
Abstract Algebra
What is x^2 - x + 20?
