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轉學考-代數
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98年 - 98 淡江大學 轉學考 代數#55938
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(h) Construct a finite field of 27 eloinctits.
其他申論題
(a) Show that if a2 + b2 is a prime in % iJicn a b√-l is a prime in R. Give an example f,o show I,hah the convcrae is not. trvio,
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【已刪除】(b) such that
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【已刪除】(c)
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.3. (15 points) (a) Construct a field F over Q such l-hal; x7 +2x + 2 has a root, in F. Find the degree of extension of F over Q.
#211900
(a) Show f,hat for any d | n, there is a subgroup of order d,
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【已刪除】(b) Show filial; if (r, n) = d、tlion ad <ar>
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【已刪除】(c) Show that, tbn subgroup <ar> has order
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【已刪除】5. (15 points) (a) Explain why non-trivial group homomorphismexisf
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【已刪除】(b) Show (Jiaf; a nori- trivial group bomomorpbism exhibitrig an example.
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(a) Show llmt every prime olcrrient in R is irrexlnciblo,
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