"Galois theory" meaning in English

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  "etymology_text": "Standardly constructed calque of French théorie de Galois (which was used as a section heading in 1870, Camille Jordan, Traité des substitutions et des équations algébriques). First appeared in print in 1893, Bulletin of the New York Mathematical Society.\nUltimately, named after French mathematician Evariste Galois (1811-1832), who first developed the theory to explore how the roots of a given polynomial equation relate to each other.",
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  "lang_code": "en",
  "pos": "noun",
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      "examples": [
        {
          "ref": "1989, G. Karpilovsky, Topics in Field Theory, North-Holland, page 299",
          "text": "In this chapter we present the Galois theory which may be described as the analysis of field extensions by means of automorphism groups.",
          "type": "quotation"
        },
        {
          "ref": "1989, Donald S. Passman, Infinite Crossed Products, Academic Press, page 297",
          "text": "The Galois theory of noncommutative rings is a natural outgrowth of the Galois theory of fields.",
          "type": "quotation"
        },
        {
          "text": "1992, Journal of Contemporary Mathematical Analysis, Volume 27, Allerton Press, page 4,\nThough often our results are prompted by the classical or parallel Galois theories, their proofs are completely different and are based on the set-theoretical approach."
        },
        {
          "ref": "2003, “Introduction”, in Leila Schneps, editor, Galois Groups and Fundamental Groups, Cambridge University Press, page ix",
          "text": "Classical Galois theory has developed a number of extensions and ramifications into more specific theories, which combine it with other areas of mathematics or restate its main problems in different situations. Three of the most important are geometric Galois theory, differential Galois theory, and Lie Galois theory, all of which have undergone very rapid development in recent years.",
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      ],
      "glosses": [
        "The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations. It provides a link between field theory and group theory: it permits certain problems in the former to be reduced to the latter, which in some respects is simpler and better understood."
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          "algebra",
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          "Galois group",
          "Galois group"
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          "Galois field",
          "Galois field"
        ],
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          "polynomial equation",
          "polynomial equation"
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          "field theory",
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        "(algebra, field theory) The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations. It provides a link between field theory and group theory: it permits certain problems in the former to be reduced to the latter, which in some respects is simpler and better understood."
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          "lang": "French",
          "sense": "branch of mathematics",
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            "feminine"
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          "word": "théorie de Galois"
        },
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          "code": "it",
          "lang": "Italian",
          "sense": "branch of mathematics",
          "tags": [
            "feminine"
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          "word": "teoria di Galois"
        }
      ],
      "wikipedia": [
        "Bulletin of the New York Mathematical Society",
        "Camille Jordan",
        "Evariste Galois",
        "Galois theory"
      ]
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      "ipa": "/ˈɡælwɑ ˈθi.əɹi/"
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  "word": "Galois theory"
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  "etymology_text": "Standardly constructed calque of French théorie de Galois (which was used as a section heading in 1870, Camille Jordan, Traité des substitutions et des équations algébriques). First appeared in print in 1893, Bulletin of the New York Mathematical Society.\nUltimately, named after French mathematician Evariste Galois (1811-1832), who first developed the theory to explore how the roots of a given polynomial equation relate to each other.",
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        },
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          "text": "1992, Journal of Contemporary Mathematical Analysis, Volume 27, Allerton Press, page 4,\nThough often our results are prompted by the classical or parallel Galois theories, their proofs are completely different and are based on the set-theoretical approach."
        },
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          "ref": "2003, “Introduction”, in Leila Schneps, editor, Galois Groups and Fundamental Groups, Cambridge University Press, page ix",
          "text": "Classical Galois theory has developed a number of extensions and ramifications into more specific theories, which combine it with other areas of mathematics or restate its main problems in different situations. Three of the most important are geometric Galois theory, differential Galois theory, and Lie Galois theory, all of which have undergone very rapid development in recent years.",
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      "glosses": [
        "The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations. It provides a link between field theory and group theory: it permits certain problems in the former to be reduced to the latter, which in some respects is simpler and better understood."
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          "algebra",
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          "Galois group",
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          "Galois field"
        ],
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          "polynomial equation",
          "polynomial equation"
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        "(algebra, field theory) The branch of mathematics dealing with Galois groups, Galois fields, and polynomial equations. It provides a link between field theory and group theory: it permits certain problems in the former to be reduced to the latter, which in some respects is simpler and better understood."
      ],
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      "sense": "branch of mathematics",
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      "word": "théorie de Galois"
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      "word": "teoria di Galois"
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  "word": "Galois theory"
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