Thé (sò͘-ha̍k)

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(Thé) ()數學 (sò͘-ha̍k)內底 (lāi-tóe)予做 (hō͘-chò)抽象 (thiu-siōng)代數 (tāi-sò͘) (ê)一支 (chi̍t-ki) (teh)研究 (gián-kiù)物京 (mi̍h-kiaⁿ)一个 (chi̍t-ê)集合 (chi̍p-ha̍p)內底的成員 (sêng-ôan)若是 (nā-sī) (ū)加法 (ka-hoat)減法 (kiám-hoat)乘法 (sêng-hoat) (kap)除法 (tû-hoat)遮的 (chia-ê)運算 (ūn-sǹg) (koh)算數 (sǹg-sò͘)的運算 (sio)siâng (á)相siâng,按呢 (án-ne)這个 (chit-ê)集合 (tio̍h)是體。

數學的 () (ēng) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbb K} (lâi)表示 (piáu-sī)體, (che) (tùi)德語 (Tek-gí)的Körper來͘ (ê)意思 (ì-sù)是 '身軀 (sin-khu)'。

正式 (Chèng-sek)定義 (tēng-gī)[修改]

體是一个有承發 (sêng-hoat)單位圓 (tan-ūi-ôan)交換環 (kau-ōaⁿ-khôan) (F, +, ×),而且 (jî-chhiáⁿ)

  • 承發單位圓1佮加法單位圓0無仝 (bô-kâng)物件 (mi̍h-kiāⁿ)
  • 準講 (chún-kóng)aFa毋是 (m̄-sī)加法單位員 (ka-hoat-tan-ūi-ôan) (lán)定著 (tiāⁿ-tio̍h)衛當 (ōe-tàng) ()F (nih)揣著 (chhōe-tio̍h)一个b (hō͘)a×b=1,抑就是 (ia̍h-tio̍h-sī) (kóng)a有乘法玉員 (ge̍k-ôan)

體的除法[修改]

(Chiàu)體的定義,F任何 (jīm-hô)1个聲援 (seng-oân)a佮毋是加法單位圓 (tan-ūi-oân)b畫棟 (ōe-tàng)宅來 (the̍h-lâi) (),除了後 (liáu-āu) (ōe)得著 (tit-tio̍h)1个 (siong)。商的定義是

解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \frac ab = } b-1×a

這个b-1b的承發玉員 (ge̍k-oân)

除法 ()交換 (kau-oāⁿ)法則 (hoat-chek) ()結合 (kiat-ha̍p)法則 (I)對加法有 (hiòng)正手爿 (chiàⁿ-chhiú-pêng)分配 (hun-phòe)法則就是 (tio̍h-sī)

解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \frac {(a+b)}{c} = \frac ac + \frac bc }

()[修改]

  1. 複雜數 (Ho̍k-cha̍p-sò͘) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbb C}一般 (it-poaⁿ)咧用的加法 (kap)乘法。伊閣有幾若的 (kúi-nā-ê)部分體 (pō͘-hūn-thé)親像 (chhin-chhiūⁿ)有理數 (iú-lí-sò͘) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbb Q}實數 (sı̍t-sò͘) 解析失敗 (Chīn-liōng iōng MathML (chhì-giām-sèng--ê):從伺服器 "https://wikimedia.org/api/rest_v1/" 收到無效的回應 ("Math extension cannot connect to Restbase.")。): {\displaystyle \mathbb R}
  2. Galois體是有盡磅 (chīn-pōng)的體,佇數論 (sò͘-lūn)電腦科學 (tiān-naú-kho-ha̍k)資訊 (chu-sìn)工程 (kang-thêng) (chin)重要 (tiōng-iàu)的物件。

性質 (Sèng-chit)[修改]