Kûn (sò͘-ha̍k)

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Kûn (Eng-gí: group) tī sò͘-ha̍k tang-tiong sī chi̍t khoán tài-sò͘ kiat-kò͘ (algebraic structure), iā chiū sī chi̍t-ê kap sǹg-hoat (operation) kiat-ha̍p ê chi̍p-ha̍p (set). Chia ê sǹg-hoat ē koat-tēng jīn-hô chi̍p-ha̍p tiong ê seng-goân kap lēng-gōa chi̍t-ê goân-sò͘ (element) ē sán-seng án-choáⁿ khoán ê tē saⁿ ê goân-sò͘ (element).

Pí-lūn kóng, chi̍t-ê "kòa ka-hoat (chi̍t khoán sǹg-hoat) ê chéng-sò͘ cho͘-sêng ê chip-ha̍p", chiū sī chi̍t-ê kûn. Chit-ê kûn tiong jīn-hô nn̄g-ê goân-sò͘ (iā chiū sī jīn-hô chéng-sò͘) ê siū ka-hoat sǹg chhut lēng-gōa ê chéng-sò͘.

Tēng-gī[siu-kái | kái goân-sú-bé]

Chim-chiok lâi-kóng, chi̍t-ê kûn "G" nā sêng-li̍p, piáu-sī i sī m̄-sī khang-ê chip-ha̍p, i ū chi̍t thò sǹg-hoat "•", chia ê chip-ha̍p kap sǹg-hoat ài móa-chio̍k sì-ê tiâu-kiāⁿ:

  • Ha̍h hong-pì-sèng (closure): Só͘-ū "G" lāi-té chhìn-chhái kéng ê "a" kap "b" in keng-kòe "a • b" sǹg--chhut-lâi ê kiat-kó mā tī "G" lāi.
  • Ha̍h kiat-ha̍p-sèng (associativity): Só͘-ū "G" lāi-té chhìn-chhái kéng ê "a", "b" kap "c", ū "(a • b) • c = a • (b • c)" koan-hē.
  • Ū tan-ūi-goân (identity element): "G" lāi-té ū chi̍t-ê goân-sò͘ "e", kap só͘-ū ê "a" ū "e • a = a • e = a" koan-hē.
  • Ū ge̍k-goân (inverse element): "G" lāi-té bí-chi̍t-ê "a", tùi-taⁿ chi̍t-ê tī"G" lāi-té ê "b", in ū "a • b = b • a = e" koan-hē, chia-ê "e" sī téng-chi̍t-hāng kóng ê tan-ūi-goân.