"Thé (sò͘-ha̍k)" pán-pún chi-kan bô-kāng--ê tē-hng

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Thé sī chi̍t-ê ū [[sêng-hoat tan-ūi-ôan]] ê [[kau-ōaⁿ-khôan]] (''F'', +, ×), jî-chhiáⁿ
Thé sī chi̍t-ê ū [[sêng-hoat tan-ūi-ôan]] ê [[kau-ōaⁿ-khôan]] (''F'', +, ×), jî-chhiáⁿ
* sêng-hoat tan-ūi-ôan 1 kap ka-hoat tan-ūi-ôan 0 sī bô-kâng ê mi̍h-kiāⁿ,
* sêng-hoat tan-ūi-ôan 1 kap ka-hoat tan-ūi-ôan 0 sī bô-kâng ê mi̍h-kiāⁿ,
* chún-kóng a ∈''F'', a m̄-sī ka-hoat-tan-ūi-ôan, lán tiāⁿ-tio̍h ōe-tàng tī ''F'' nih chhōe-tio̍h chi̍t-ê b, hō͘ a×b=1, iah-tio̍h-sī kóng a ū seng-hoat ge̍k-ôan.
* chún-kóng a∈''F'', a m̄-sī ka-hoat-tan-ūi-ôan, lán tiāⁿ-tio̍h ōe-tàng tī ''F'' nih chhōe-tio̍h chi̍t-ê b, hō͘ a×b=1, iah-tio̍h-sī kóng a ū seng-hoat ge̍k-ôan.

== Thé ê tû-hoat ==
Chiàu thé ê tēng-gī, ''F'' ê 2-ê jīm-hô 1-ê seng-oân a kap m̄-sī ka-hoat tan-ūi-oân ê b ōe-tàng the̍h-lâi tû, tû liáu-āu ōe tit-tio̍h 1-ê [[siong]]. Siōng ê tēng-gī sī
:::<math>\frac ab = </math>b<sup>-1</sup>&times;a
Chit-ê b<sup>-1</sup> sī b ê sêng-hoat ge̍k-oân.

Tû-hoat bô kau-oāⁿ hoat-chek mā bô kiat-ha̍p hoat-chek. I tùi ka-hoat ū hiòng chiaⁿ-chhiú-pêng ê [[hun-phòe hoat-chek]], tio̍h-sī
::: <math>\frac {(a+b)}{c} = \frac ac + \frac bc </math>

== Lē ==
# [[Hok-cha̍p-sò͘ ]] <math> \mathbb C</math> kap it-poaⁿ teh ēng ê ka-hoat kap seng-hoat. I koh ū kúi-nā-ê pō͘-hūn-thé, chhin-chhiūⁿ [[iú-lí-sò͘]] kap [[sı̍t-sò͘]].
# [[Galois thé]]


== Sèng-chit ==
== Sèng-chit ==

2006-nî 4-goe̍h 13-ji̍t (pài-sì) 02:57 ê siu-tēng-pún

Thé sī sò͘-ha̍k lāi-tóe hō͘-chò thiu-siōng tāi-sò͘ ê chi̍t-ki teh giám-kiù ê mi̍h-kiaⁿ, chi̍t-ê chi̍p-ha̍p lāi-tóe ê sêng-ôan nā-sī ū ka-hoat, kiám-hoat, sêng-hoat kap tû-hoat, chia-ê ūn-sǹg koh kap sǹg-sò͘ ê ūn-sǹg sio-siâng-á sio-siâng, án-ne chit-ê chi̍p-ha̍p tio̍h sī thé.

Sò͘-ha̍k ê lē sī ēng lâi piáu-sī thé, che sī tùi Tek-gí ê Körper lâi-·ê, ì-sù sī 'sin-khu'.

Chèng-sek ê tēng-gī

Thé sī chi̍t-ê ū sêng-hoat tan-ūi-ôan ê kau-ōaⁿ-khôan (F, +, ×), jî-chhiáⁿ

  • sêng-hoat tan-ūi-ôan 1 kap ka-hoat tan-ūi-ôan 0 sī bô-kâng ê mi̍h-kiāⁿ,
  • chún-kóng a∈F, a m̄-sī ka-hoat-tan-ūi-ôan, lán tiāⁿ-tio̍h ōe-tàng tī F nih chhōe-tio̍h chi̍t-ê b, hō͘ a×b=1, iah-tio̍h-sī kóng a ū seng-hoat ge̍k-ôan.

Thé ê tû-hoat

Chiàu thé ê tēng-gī, F ê 2-ê jīm-hô 1-ê seng-oân a kap m̄-sī ka-hoat tan-ūi-oân ê b ōe-tàng the̍h-lâi tû, tû liáu-āu ōe tit-tio̍h 1-ê siong. Siōng ê tēng-gī sī

b-1×a

Chit-ê b-1 sī b ê sêng-hoat ge̍k-oân.

Tû-hoat bô kau-oāⁿ hoat-chek mā bô kiat-ha̍p hoat-chek. I tùi ka-hoat ū hiòng chiaⁿ-chhiú-pêng ê hun-phòe hoat-chek, tio̍h-sī

  1. Hok-cha̍p-sò͘ kap it-poaⁿ teh ēng ê ka-hoat kap seng-hoat. I koh ū kúi-nā-ê pō͘-hūn-thé, chhin-chhiūⁿ iú-lí-sò͘ kap sı̍t-sò͘.
  2. Galois thé

Sèng-chit

  • Chi̍t-ê thé F lāi-tóe m̄-sī 0 ê sêng-ôan chiâⁿ-sêng ê chi̍p-ha̍p ( it-poaⁿ sī kì-chò F×), kap F ê sêng-hoat chiâⁿ-chò chi̍t-ê abelian kûn. F× ê pō͘-hūn-kûn sī sûn-khôan-kûn.
  • Thé ê piau-sò͘ nā m̄-sī 0 tio̍h-sī sò͘-sò͘.
  • Iú-hān-thé ê seng-ôan sò͘-ba̍k it-tēng sī sò͘-sò͘ ê chéng-sò͘ chhù-hong.
  • Kā thé tòng-chò khôan, i kan-taⁿ u 2-ê lí-sióng, {0} kap i ka-tī.