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Abstract Algebra
Q. Give counter example to that
Every (Greatest Common Divisor ) Domain is not UFD (Unique Factorization Domain)
Every (Greatest Common Divisor ) Domain is not UFD (Unique Factorization Domain)
Abstract Algebra
Q. Let A and B be two ideals of ring R such that R=A⊕B show that R/A ≅B (R factor A is isomorphic to B) and
R/B ≅A (R factor B is isomorphic to A).
R/B ≅A (R factor B is isomorphic to A).
Abstract Algebra
what is isomorphism?
Abstract Algebra
how many associative binary operation does set with 3 elements have?
Abstract Algebra
Find the order of y2. Is the subgroup hy2i normal? Justify your answer.
Abstract Algebra
Calculate (2x+3)(3x+4) in Z5[x].
Abstract Algebra
4[8-{5\4}+(5+7)-7]
Abstract Algebra
Which of the following subsets are subgroups of D12? Justify your answer.
i) {x, y, xy, y
2
, y
3
, e} ii) {xy, xy2
, y
2
, e} iii) {x, y
3
, xy3
, e}
i) {x, y, xy, y
2
, y
3
, e} ii) {xy, xy2
, y
2
, e} iii) {x, y
3
, xy3
, e}
Abstract Algebra
Factorise 10 in two ways in Z[
√
−6]. Hence, show that Z[
√
−6] is not a UFD
√
−6]. Hence, show that Z[
√
−6] is not a UFD
Abstract Algebra
) Let H = h(1 2)i and K = h(1 2 3)i be subroups of S3. Check that S3 = HK. Is S3 the internal
direct product of H and K? Justify your answer.
direct product of H and K? Justify your answer.
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#339914 on Dec 2023
#339914 on Dec 2023