"algebraic K-theory" meaning in All languages combined

{
  "head_templates": [
    {
      "args": {
        "1": "-",
        "head": "algebraic K-theory"
      },
      "expansion": "algebraic K-theory (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms containing italics",
          "parents": [
            "Terms containing italics",
            "Terms by orthographic property",
            "Terms by lexical property"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "French links with redundant target parameters",
          "parents": [
            "Links with redundant target parameters",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "German links with redundant target parameters",
          "parents": [
            "Links with redundant target parameters",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "higher algebraic K-theory"
        }
      ],
      "examples": [
        {
          "ref": "1999, E. M. Friedlander, “Lecture VII. Beilinson's vision”, in H. Bass, A. O. Kuku, C. Pedrini, editors, Algebraic K-theory And Its Applications, World Scientific, page 61",
          "text": "Algebraic cycles are typically studied by imposing one of several equivalence relations. The equivalence relation most relevant for algebraic K-theory is rational equivalence.",
          "type": "quotation"
        },
        {
          "ref": "2013, Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, American Mathematical Society, page ix",
          "text": "Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K#x5F;0 of a category and uses explicit algebraic presentations and higher algebraic K-theory which requires topological or homological machinery to define.",
          "type": "quotation"
        },
        {
          "text": "2014, Daniel Scott Farley, Ivonne Johanna Ortiz, Algebraic K-theory of Crystallographic Groups, Springer, Lecture Notes in Mathematics 2113, page 1,\nAlgebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. […] Algebraic K-theory plays an important part in many areas of mathematics, especially number theory, algebraic topology and algebraic geometry."
        }
      ],
      "glosses": [
        "K-theory studied from the point of view of algebra."
      ],
      "id": "en-algebraic_K-theory-en-noun-iwZEi5QI",
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "K-theory",
          "K-theory"
        ],
        [
          "algebra",
          "algebra"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) K-theory studied from the point of view of algebra."
      ],
      "related": [
        {
          "word": "K-theory"
        },
        {
          "word": "topological K-theory"
        },
        {
          "word": "K-group"
        }
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fr",
          "lang": "French",
          "sense": "K theory studied from the point of view of algebra",
          "tags": [
            "feminine"
          ],
          "word": "K-théorie algébrique"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "K theory studied from the point of view of algebra",
          "tags": [
            "feminine"
          ],
          "word": "algebraische K-Theorie"
        }
      ],
      "wikipedia": [
        "algebraic K-theory"
      ]
    }
  ],
  "word": "algebraic K-theory"
}

{
  "derived": [
    {
      "word": "higher algebraic K-theory"
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "head": "algebraic K-theory"
      },
      "expansion": "algebraic K-theory (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "K-theory"
    },
    {
      "word": "topological K-theory"
    },
    {
      "word": "K-group"
    }
  ],
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms containing italics",
        "English terms with quotations",
        "English uncountable nouns",
        "French links with redundant target parameters",
        "German links with redundant target parameters",
        "en:Algebraic geometry"
      ],
      "examples": [
        {
          "ref": "1999, E. M. Friedlander, “Lecture VII. Beilinson's vision”, in H. Bass, A. O. Kuku, C. Pedrini, editors, Algebraic K-theory And Its Applications, World Scientific, page 61",
          "text": "Algebraic cycles are typically studied by imposing one of several equivalence relations. The equivalence relation most relevant for algebraic K-theory is rational equivalence.",
          "type": "quotation"
        },
        {
          "ref": "2013, Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, American Mathematical Society, page ix",
          "text": "Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K#x5F;0 of a category and uses explicit algebraic presentations and higher algebraic K-theory which requires topological or homological machinery to define.",
          "type": "quotation"
        },
        {
          "text": "2014, Daniel Scott Farley, Ivonne Johanna Ortiz, Algebraic K-theory of Crystallographic Groups, Springer, Lecture Notes in Mathematics 2113, page 1,\nAlgebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. […] Algebraic K-theory plays an important part in many areas of mathematics, especially number theory, algebraic topology and algebraic geometry."
        }
      ],
      "glosses": [
        "K-theory studied from the point of view of algebra."
      ],
      "links": [
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "K-theory",
          "K-theory"
        ],
        [
          "algebra",
          "algebra"
        ]
      ],
      "raw_glosses": [
        "(algebraic geometry) K-theory studied from the point of view of algebra."
      ],
      "tags": [
        "uncountable"
      ],
      "topics": [
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "algebraic K-theory"
      ]
    }
  ],
  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "K theory studied from the point of view of algebra",
      "tags": [
        "feminine"
      ],
      "word": "K-théorie algébrique"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "K theory studied from the point of view of algebra",
      "tags": [
        "feminine"
      ],
      "word": "algebraische K-Theorie"
    }
  ],
  "word": "algebraic K-theory"
}