"Thé (sò͘-ha̍k)" pán-pún chi-kan bô-kāng--ê tē-hng
→Lē: ho̍k-sò͘ kái tńg-lâi ho̍k-cha̍p-sò͘ |
~ r2.5) (bot ka-thiam: ar, bg, ca, da, de, el, eo, es, et, fa, fi, fr, he, hr, hu, id, io, it, ja, ko, nl, no, pl, pms, pt, ro, ru, scn, sk, sl, sr, sv, tr, uk, vi, zh, zh-classical |
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Tē 27 chōa: | Tē 27 chōa: | ||
[[Category:Sò͘-ha̍k]] |
[[Category:Sò͘-ha̍k]] |
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[[ar:حقل رياضي]] |
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[[bg:Поле (алгебра)]] |
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[[ca:Cos (matemàtiques)]] |
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[[da:Legeme (algebra)]] |
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[[de:Körper (Algebra)]] |
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[[el:Σώμα (άλγεβρα)]] |
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[[en:Field (mathematics)]] |
[[en:Field (mathematics)]] |
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[[eo:Korpo (algebro)]] |
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[[es:Cuerpo (matemática)]] |
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[[et:Korpus (matemaatika)]] |
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[[fa:میدان (ریاضی)]] |
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[[fi:Kunta (matematiikka)]] |
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[[fr:Corps commutatif]] |
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[[he:שדה (מבנה אלגברי)]] |
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[[hr:Polje (matematika)]] |
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[[hu:Test (algebra)]] |
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[[id:Medan (matematika)]] |
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[[io:Feldo (algebro)]] |
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[[it:Campo (matematica)]] |
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[[ja:体 (数学)]] |
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[[ko:체 (수학)]] |
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[[nl:Lichaam (Ned) / Veld (Be)]] |
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[[no:Kropp (matematikk)]] |
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[[pl:Ciało (matematyka)]] |
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[[pms:Camp (matemàtica)]] |
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[[pt:Corpo (matemática)]] |
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[[ro:Corp (matematică)]] |
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[[ru:Поле (алгебра)]] |
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[[scn:Corpu (matimàtica)]] |
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[[sk:Pole (algebra)]] |
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[[sl:Obseg (algebra)]] |
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[[sr:Поље (математика)]] |
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[[sv:Kropp (algebra)]] |
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[[tr:Cisim (cebir)]] |
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[[uk:Поле (алгебра)]] |
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[[vi:Trường (đại số)]] |
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[[zh:域 (數學)]] |
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[[zh-classical:域 (代數)]] |
2011-nî 1-goe̍h 21-ji̍t (pài-gō·) 22:42 ê siu-tēng-pún
Thé sī sò͘-ha̍k lāi-tóe hō͘-chò thiu-siōng tāi-sò͘ ê chi̍t-ki teh gián-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, ia̍h-tio̍h-sī kóng a ū sêng-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. Siong 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 chiàⁿ-chhiú-pêng ê hun-phòe hoat-chek, tio̍h-sī
Lē
- Ho̍k-cha̍p-sò͘ kap it-poaⁿ teh ēng ê ka-hoat kap sêng-hoat. I koh ū kúi-nā-ê pō͘-hūn-thé, chhin-chhiūⁿ iú-lí-sò͘ kap sı̍t-sò͘ .
- 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×), 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.