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From: yosida@parkcity.ne.jp (=?ISO-2022-JP?Q?=3F=1B$B!-=1B(B=3FV?=)
Newsgroups: fj.sci.math
Subject: Re: =?ISO-2022-JP?Q?=1B$B4D#R$+$i#R<+=3FH$X$N=3D`F17=3F=1B(B?=
Date: 7 Jun 2003 22:32:30 -0700
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Xref: ccsf.homeunix.org fj.sci.math:178

asume R is not {0}.

A)	0(a)=(0-0)(a)=0(a)-0(a)=0

B)for non-zero f, there are some a
with f(a) is non-zero.
and	 1 f(a)
	=f(a)
	=f(1 a)
	=f(1) f(a),
so	f(1)=1

C)	1+1 is not 1
so	g(1)=1+1 implies g=0

D)for non-zero f, C)
and	(f+f)(1)=f(1)+f(1)=1+1,
	f+f=0
---
yosida@parkcity.ne.jp

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