Subject: Re: [HM] unitary rings
From: Prof. Dr. Jochen Ziegenbalg (ye12@rz.uni-karlsruhe.de)
Date: Tue May 23 2000 - 09:09:38 EDT
On Mon, 22 May 2000, Julio Gonzalez Cabillon wrote:
> Estimado Francisco:
>
> David M. Burton y Donovan H. van Osdol publicaron en "Learn from
> the Masters" [MAA, 1995 -- ISBN 0-88385-703-0] un interesante
> articulo titulado "Toward the Definition of an Abstract Ring"
> [pp 241-251]. Las referencias a los trabajos originales citados
> en la bibliografia son tambien de gran utilidad.
>
> Saludos desde Montevideo, Julio
One of the masters to learn from is certainly N. Jacobson. In his "Basic
Algebra" (W.H. Freeman & Company) he suggests the term "rngs" (suggested
pronunciation: "rungs") for rings without a unit element and shows that
any rng without a unit can be embedded in a ring (with unit) in a
canonical way. Maybe, this is the reason why most authors include the
existence of a unit into the definition of a ring right from the start.
Greetings from Karlsruhe,
Jochen Ziegenbalg
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