Re: Embedding Boolean Algebras

From: Noel Vaillant (vaillant_at_probability.net)
Date: 10/31/04 

Date: Sun, 31 Oct 2004 16:51:41 GMT

> > This applies in particular to Boolean algebras (which are just
> > commutative rings in which every element is idempotent, i.e. a^2=a)
>
> Itdoesnot,Booleanalgebrashave a + a = a.

Sure, we have a \/ a = a , but if you define:

a+b = a'b \/ ab'

Then (B,+, /\) is a commutative ring (with unit) in which every element is
idempotent. Hence Krull's theorem applies.

Every Boolean algebra has a maximal (proper) ideal.