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102年 - 102 淡江大學 轉學考 代數#53069
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題組內容
6. (20 pts)
(a) Show that x
3
+ x + 1 is irreducible in Z
5
[x].
其他申論題
3. (12 pts) Suppose G = {e, a, 6, c} is a group of order 4; but it contains no element of order 4. Write out the operation table for G.
#193078
(a) Prove that every finite integral domain is a field.
#193079
(b) Give an example of an integral domain which is not a field.
#193080
5. (12 pts) Show that the principal ideal (x — 1) in Z[x] is prime but not maximal. .
#193081
(b) Let R be the quotient ring Z5[x]/ (x3 +x + 1). How many elements are there in R1 Is R a field? Please justify your answer
#193083
【已刪除】1 求極限
#193084
【已刪除】2.若a, b是兩實數使得定積分,最大，求b — a。
#193085
【已刪除】3.求定積分
#193086
4.求函數 f(x) - (x2 + l)sinx；的微分。
#193087
【已刪除】5.求極限
#193088
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