I-Abstract algebra

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I-Abstract algebra lolunye uhlobo lakwa-math olufunda nzulu ngezakhiwo ze-algebra nekuthiwa yi-algebraic structures. Ezi zakhiwo ziquka:  

  • amaqela abizwa ngokuba zii-groups
  • Izazinge ekuthiwa zii-rings
  • ii-fields
  • ii-vector spaces
  • ii-algebras
  • i-Boolean algebra

Yinto eqhelekileyo ukwakhela i-theori kuhlobo olunye lwesakhiwo esinye, njengakwi-group theory okanye kwi-category theory.

Injongo yetheori kwi-concept nganye kukuza nenkcazo epheleleyo necacileyo nge- concept, imizekelo yayo, izakhiwana eziphuma kuyo, iindlela zokunxulumanisa imizekelo ye-concept eyahlukeneyo ngokwakwa-algebra(ically) (ezi ke zibizwa ngokuba zii-morphisms kwezinye iimeko), kunye nokusetyenziswa kwee-concepts, macalana omabini ngaphakathi kwitheori yayo, nangaphandle kwamanye amabakala amanye amabakala  emathematics.

Ngexesha lembali, amabakala ngamabakala akwa-mathematics asebenzise ii--algebras. Ii-algebras zimalunga nokufumana okanye zixele ngokucacileyo nokuchanekileyo imigaqo yokubala ngee-formulas nangee-expressions ezithile kwamathematics.  Olunye uhlobo lwe-algebra (nolungelilo olu-abstract) yi-elementary algebra, umzekelo. 

Examples[tshintsha | edit source]

  • Ukusombulula ii-equations ngee-variables ezininzi. Oku kukhokelela kwii-matrices, ii-determinants kunye nee-linear algebra.
  • Ukufumana ii-formulas ze-polynomial equations. Oku kukhokhelela ekufumaneni (amaqela) ii-groups, njege-expression ye-symmetry.
  • I-Quadratic kunye ne-higher-degree equations kunye nee-Diophantine equations - ingakumbi xa i-Fermat's last theorem yayi-proved ikhokhelela kwinkcazo epheleleyo ye-rings, kunye nee-ideals.