See algebraic number theory in All languages combined, or Wiktionary
Download JSON data for algebraic number theory meaning in English (4.9kB)
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"ref": "1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241",
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"ref": "2008, Steven H. Weintraub, Factorization: Unique and Otherwise, CRC Press, page 143",
"text": "The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory.",
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"ref": "2013, Mak Trifković, Algebraic Theory of Quadratic Numbers, Springer, page v",
"text": "Elementary arithmetic studies divisibility and factorization of ordinary integers, Algebraic number theory considers the same questions for algebraic numbers, solutions to polynomial equations with integer coefficients. In this setting, (un)fortunately, the uniqueness of prime factorization no longer holds. Remedying and measuring its failure is the starting point of algebraic number theory.",
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"The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
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"(mathematics, number theory) The branch of number theory in which number-theoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra."
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"sense": "branch of number theory concerning algebraic number fields",
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"sense": "branch of number theory concerning algebraic number fields",
"word": "代數數論"
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"code": "cmn",
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"roman": "dàishùshùlùn",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代数数论"
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"sense": "branch of number theory concerning algebraic number fields",
"word": "հանրահաշվական թվերի տեսություն"
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"sense": "branch of number theory concerning algebraic number fields",
"word": "代數數論"
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{
"code": "cmn",
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"roman": "dàishùshùlùn",
"sense": "branch of number theory concerning algebraic number fields",
"word": "代数数论"
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"sense": "branch of number theory concerning algebraic number fields",
"tags": [
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"sense": "branch of number theory concerning algebraic number fields",
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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