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Abstract Algebra
Considere the ideal I=<x²-4x+3,x³+3x²-x-3> of the ring Q[x]. Find a polynomial p such that I=<p>.Is Q[x]/I a field? Give reasons for your answer.
Abstract Algebra
Let R be a commutative Ring with identity.let I and J be ideals of R such that I+J=Show that IJ= intersection of I and J.
Abstract Algebra
Give two distinct maximal ideals in the polynomial ring Q[x] with justification.
Abstract Algebra
Prove that R⁵/R² is isomorphic to R³.
Abstract Algebra
Give an example of infinite ring of characteristic 7.
Abstract Algebra
Show that the ideal <x^2+1> is not prime in Z2[x]
Abstract Algebra
Assume that (G,*) is a group and that (H,*) and (K,*) are subgroups of (G,*).Prove that (H intersects K , *) is a subgroup of (G,*)
Abstract Algebra
Prove that if (G,*) is a finite group, and g is an element of G, then there exists a positive integer n such that g^n =e
Abstract Algebra
Show that d:Q[x]\{0}→NU{0}:d(f)=2^deg f is a Euclidean valuation on Q[x].
Abstract Algebra
Find the quotient field of integral domain {a+ib such that a,b belongs to Z}
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#339914 on Dec 2023
#339914 on Dec 2023