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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
4. (24 pts)
(a) Prove that every finite integral domain is a field.
其他申論題
【已刪除】 (a) Suppose p is a prime number and a is an integer, (a,p) — 1. Prove that ap~11 (mod p).
#193075
(b) What is the remainder when 3535 is divided by 37?
#193076
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
(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
(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
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