Re: infinite sequence ring theory problem

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 03/14/05 

Date: Mon, 14 Mar 2005 22:31:17 +0000 (UTC)

In article <1110839220.507728.309860@f14g2000cwb.googlegroups.com>,
 <jamesdickerson00@hotmail.com> wrote:
>1) Show that there exists an infinite sequence a=a1,a2,a3,.... of
>nonzero elements of R such taht a_j belongs to a_iRa_i whenever 1 less
>than equal i less than j.

Seems particularly difficult if you don't tell us what R is! This is
certainly false in some rings, so you must have some specific ring to
which this is supposed to apply. But I am at a loss to know which
one. There are, after all, so many to choose from...

>2) Let S={a_i|1 less than equal i less than infinity} as in part 1. IF
>I,J are ideals of R with I intersect S not equal to the empty set not
>equal to J intersect S, show that IJ intersect S is not the empty set.

As above. 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
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Arturo Magidin
magidin@math.berkeley.edu
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