- 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 - 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 > as a new member of this group,

Some of the information below is summarized from postings on the History

> 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)?

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- 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