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Abstract Algebra
b) Let G be a group, H∆ G and β≤ G/H . Let A ={x∈G | Hx∈β}. Show that
i) A≤G , ii) H∆ A , iii) β= A/H
i) A≤G , ii) H∆ A , iii) β= A/H
Abstract Algebra
Let R be an integral Domain then deg(fg)=degf+degg
Abstract Algebra
R be a commutative ring with identity iff R[[X]] is commutative ring with identity
Abstract Algebra
Is the polynomial ring R[X] a subring of R[[X]]?
Abstract Algebra
let R be a commutative Ring with identity a formal power series f(X) is invertible in R[[x]] if and only if the constant term f0 has an inverse in R
Abstract Algebra
Prove that R ^n/R^m~=R^n-m as groups, where n, m belongs to N such that n>=m.
Abstract Algebra
if a=b(mod r) and a=b(mod s) then a=b(mod [r,s])
Abstract Algebra
Find the least nonnegative residue of 365 (mod 5)
Abstract Algebra
Find the smallest a that is congruent to 3412 (mod4)
Abstract Algebra
Prove that field has no zero divisors
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