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

pheng-im, wiki-hoà, ho̍k-cha̍p-sò͘ -> ho̍k-sò͘
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(pheng-im, wiki-hoà, ho̍k-cha̍p-sò͘ -> ho̍k-sò͘)
'''Thé''' sī sò͘-ha̍k lāi-tóe hō͘-chò [[thiu-siōng tāi-sò͘]] ê chi̍t-ki teh giámgián-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 <math>\mathbb K</math> lâi piáu-sī thé, che sī tùi Tek-gí ê Körper lâi-·ê, ì-sù sī 'sin-khu'.
Thé sī chi̍t-ê ū [[sêng-hoat tan-ūi-ôan]] ê [[kau-ōaⁿ-khôan]] (''F'', +, &times;), 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''&times;''b''=1, iahia̍h-tio̍h-sī kóng ''a'' ū seng-hoat ge̍k-ôan.
 
== Thé ê tû-hoat ==
Chiàu thé ê tēng-gī, ''F'' 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]]. SiōngSiong 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 chiaⁿchiàⁿ-chhiú-pêng ê [[hun-phòe hoat-chek]], tio̍h-sī
::: <math>\frac {(a+b)}{c} = \frac ac + \frac bc </math>
 
== Lē ==
# [[Hok-cha̍pHo̍k-sò͘ ]] <math> \mathbb C</math> kap it-poaⁿ teh ēng ê ka-hoat kap sengsêng-hoat. I koh ū kúi-nā-ê pō͘-hūn-thé, chhin-chhiūⁿ [[iú-lí-sò͘]] <math>\mathbb Q</math> kap [[sı̍t-sò͘]] <math>\mathbb R</math>.
# [[Galois thé]] sī ū chīn-pōng ê thé, tī sò͘-lūn, tiān-naú-kho-ha̍k kap chu-sìn kang-thêng sī chin tiōng-iàu ê mi̍h-kiāⁿ.
 
== 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''<sup>&times;</sup>), kap ''F'' ê sêng-hoat chiâⁿ-chò chi̍t-ê [[abelian kûn]]. ''F''<sup>&times;</sup> 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.
 
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