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102年 - 102 淡江大學 轉學考 代數#53069
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5. (12 pts) Show that the principal ideal (x — 1) in Z[x] is prime but not maximal. .
其他申論題
2. (12 pts) Prove or disprove: If G is a group of order 53, then G must be cyclic.
#193077
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
(a) Show that x3 + x + 1 is irreducible in Z5 [x].
#193082
(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
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