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.