共同構造的幸福
2023-9-30 16:16:01
Assume R[x] is an PID
R is a field
因為R 係ID,所以ideal of x is prime ideal(by R is PID, R is ID)
因為R[x]係PID和 (x) obviously is non-zero ideal,所以(x) is maximal ideal
故此R/(x) ,(x)是zero ideal和R/(x)是unit ideal,只有兩個ideal,R adjoins with x / ideal of x is isomorphic to R,所以R便是field
共同構造的幸福
2023-9-30 16:17:44
有冇話前面悶 中後勁好睇
共同構造的幸福
2023-9-30 16:19:20
故此R[x]/(x) ,(x)是zero ideal和R[x]/(x)是unit ideal,只有兩個ideal,R adjoins with x / ideal of x is isomorphic to R,所以R便是field
打漏咗
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潘朵拉的盒拓撲
2023-9-30 16:21:02
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潘朵拉的盒拓撲
2023-9-30 16:21:28
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共同構造的幸福
2023-9-30 16:21:39
Assume R[x] is an PID
R is a field
因為R adjoins with x / ideal of x is isomorphic to R,R 係ID