Algebra abstracta







Evaristus Galois principia theoriae catervarum invenit, pars magna algebrae abstractae


Algebra abstracta (sive algebra generalis) est pars mathematicae quae de structuris tractat, sicut catervis et corporibus. Mathematici tales structuras recognoverunt cum similia problemata solvere conarentur. Exempli gratia, permutationes vel symmetriae figurarum (et compositio), integri (et additio), matrices (et eorum additio) omnes sunt copiae, cum operatione binario commutativo: haec est structura quam gregem Abelianum nominamus.


Structurae maximi momenti hae sunt:



  • Anellus

  • Calculus differentialis

  • Corpus


  • Grex vel caterva; theoria catervarum de eis tractat.

  • Matrix


  • Spatium vectorum; algebra linearis de eis tractat. Spatium vectorum dimensionis infinitae est spatium Hilbertianum et pars est analysis.


Scilicet necesse est theoriam copiarum habere ante theoriam algebrae vel theoriam numerorum. Et theoria categoriarum, plus generaliter, de structura ipsa tractat.


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mathematica
Haec stipula ad mathematicam spectat. Amplifica, si potes!



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