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words of the day

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  • jensd99
    Hello, as a new member of this group, I d like to pose a question: Does anybody know, why the algebraic ring is called ring and the field called a field (in
    Message 1 of 4 , Sep 14, 2007
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      Hello,

      as a new member of this group, I'd like to pose a question: Does
      anybody know, why the algebraic ring is called ring and the field
      called a field (in german a body)?

      My main interests are in algebra, number theory and reduction systems.
      I am a researcher and try to establish a new kind of method ..

      Regards
      Jens
    • Melvin Henriksen
      If my memory is accurate, the name ringe appeared first in 1915 or 1916 in a paper of Fraenkel. It is not in Weber s Algebra , which does contain the word
      Message 2 of 4 , Sep 14, 2007
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        If my memory is accurate, the name "ringe" appeared first in 1915 or
        1916 in a paper of Fraenkel. It is not in Weber's "Algebra", which does
        contain the word "korper" (field). I am ignorant of when this latter
        concept was first used. I will try to find out more, but an historian of
        mathematics could probably do it faster.
        Melvin Henriksen
        jensd99 wrote:
        >
        >
        > Hello,
        >
        > as a new member of this group, I'd like to pose a question: Does
        > anybody know, why the algebraic ring is called ring and the field
        > called a field (in german a body)?
        >
        > My main interests are in algebra, number theory and reduction systems.
        > I am a researcher and try to establish a new kind of method ..
        >
        > Regards
        > Jens
        >
        >


        --
        Melvin Henriksen
        Harvey Mudd College
        Ph: 909 626 3676
      • Keith A. Kearnes
        ... Some of the information below is summarized from postings on the History of Math pages at The Math Forum @Drexel. (I haven t tried to verify its
        Message 3 of 4 , Sep 18, 2007
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          > as a new member of this group,
          > I'd like to pose a question: Does
          > anybody know, why the algebraic ring is called ring and the field
          > called a field (in german a body)?

          Some of the information below is summarized from postings on the History
          of Math pages at The Math Forum @Drexel. (I haven't tried to verify its
          correctness.)

          Field:
          The word "koerper" for "field" was coined by Dedekind.
          It first appeared in the second edition of Dirichlet's "Vorlesungen ueber
          Zahlentheorie", Braunschweig, 1871. By the time of the fourth edition
          Dedekind had added a footnote explaining his choice of the word "koerper",
          apparently in response to criticism from Kronecker, who was using the term
          "Rationalitaetsbereich" instead. "Rationalitaetsbereich" can be translated
          as "realm (or area or field) of rationality". Apparently the first use of
          the English word "field" in this context is in E. H. Moore's, "A
          doubly-infinite system of simple groups", Math. Papers Read at the
          International Mathematical Congress Chicago 1893, 208-242. New York 1896

          Ring:
          (Here I'll just copy a message from the pages cited above.)

          [Beginning of quote]

          Date: Sat, 7 Dec 1996 11:22:58 -0500
          From: Julio Gonzalez Cabillon
          Subject: Re: Rings

          Browsing through the archives I found that some time ago there was an
          interest in the term "ring".

          Richard Dedekind was first to introduce the CONCEPT of *ring*. The TERM
          "Zahlring" was coined by David Hilbert in the context of algebraic
          number theory [See "Die Theorie der algebraische Zahlk\"orper",
          _Jahresbericht der Deutschen Mathematiker Vereiningung_, Vol. 4, 1897].

          And the first ABSTRACT definition of a *ring* was given in 1914 by
          A. A. Fraenkel in an essay in _Journal f\"ur die reine und angewandte
          Mathematik_ (A. L. Crelle), vol. 145, 1914. (The AXIOMATIC definition
          currently used nowadays appeared three years later.)

          Why Hilbert christened the concept with that name is unknown, though
          as usual many speculations have been made--the most plausible, perhaps,
          being *Zahlenring* or *ring of numbers* in the context of the ring
          of integers modulo 'n'. Strong closure and circular possibility might
          be the reason.

          [End of quote]





          --
          Keith A. Kearnes Email: kearnes@...
          Department of Mathematics WWW: http://spot.colorado.edu/~kearnes
          University of Colorado Direct Phone: (303) 492-5203
          395 UCB Dept Phone: (303) 492-3613
          Boulder, CO 80309-0395 Fax: (303) 492-7707
        • jensd99
          Many thanks for the useful explanations! Meanwhile when sitting on the terrace I came across a tile, which is a physical body and an open set of atoms in my
          Message 4 of 4 , Sep 18, 2007
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            Many thanks for the useful explanations!

            Meanwhile when sitting on the terrace I came across a tile, which is a
            physical body and an open set of atoms in my opinion. Taking the
            direct sum + and the intersection * of sets it might be a mathemetical
            korper (body) too...

            Regards
            Jens
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