阿摩線上測驗
登入
首頁
>
轉學考-代數
>
98年 - 98 淡江大學 轉學考 代數#55938
>
題組內容
4. (20 poinl.s) Let G =- <a> be a cyclic grovip of order n.
(a) Show f,hat for any d | n, there is a subgroup of order d,
其他申論題
【已刪除】(b) such that
#211898
【已刪除】(c)
#211899
.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
(h) Construct a finite field of 27 eloinctits.
#211901
【已刪除】(b) Show filial; if (r, n) = d、tlion ad <ar>
#211903
【已刪除】(c) Show that, tbn subgroup <ar> has order
#211904
【已刪除】5. (15 points) (a) Explain why non-trivial group homomorphismexisf
#211905
【已刪除】(b) Show (Jiaf; a nori- trivial group bomomorpbism exhibitrig an example.
#211906
(a) Show llmt every prime olcrrient in R is irrexlnciblo,
#211907
(b) Suppose ihnl R is a PID. Show tlmt, every irreducible element in /i! is a prime.
#211908
阿摩線上測驗
登入
阿摩線上測驗
登入