Date: Feb 5, 2013 3:53 AM
Author: William Elliot
Subject: Re: Finite Rings
On Mon, 4 Feb 2013, Arturo Magidin wrote:
> On Monday, February 4, 2013 10:55:03 AM UTC-6, Arturo Magidin wrote:
> > The only two books I have that do not allow 1=0 are: Zariski and
> > Samuel's "Commutative Algebra", which restricts the use of the term
> > "identity" to rings that are not nullrings; and Lam's "A First Course
> > in Noncommutative rings" and "Lectures on Rings and Modules", which
> > specifies this explicitly in the introduction.
> Added: Note, however, that the zero ring does not qualify as a "ring"
> under Lam's definitions, so it cannot be an example. So the only book I
> have that both allows the 0 ring, and *does not* recognize the 0 ring as
> a ring with identity, is Zariski-Samuel. It also happens to be by far
> the oldest, having been published originally in 1958.
Much ado about nothing.
One man's heresy is another's definition.
Yet the problem still remains problematic.