轉學考-代數題庫  下載題庫

96 年 - 96 淡江大學轉學考代數#55974　

選擇:0題,非選:7題我要補題回報試卷錯誤

【非選題】
1.1. Prove that {1,-1, i, -i} is a cyclic group under the usual multiplication. (10%)

【非選題】
2.2. Show that a group G is abelian if for each g in G g² = e, where e is the identity of G (15%)

【非選題】
3.3. Show that any group order 7 is cyclic. (15%)

【非選題】
4.4. Let G be a group such that 200 ＜ |G| ＜ 300. Suppose G has subgroups of order 21 and 33, find |G|. (15%)

【非選題】
5.5. Let R be a commutative ring with identity 1. Prove that an ideal P is a prime if and only if

is an integral domain. (15%)

【非選題】
6.6. Prove that Z is a PID, where Z is the set of integers. (15%)

【非選題】
7.7. Up to isomorphism, find all abelian groups of order 12. (15%)

22. 現今民主制度的發展中，有三部重要文獻，(甲)人權宣言(乙)獨立宣言(丙)權利法案。請問：此三者出現的順序為何？ (A)甲乙丙　(B)甲丙乙　(C)丙乙�...