Rings, Restatement of earlier problem

From: Tony (Ttiger222_at_hotmail.com)
Date: 01/30/05 

Date: Sat, 29 Jan 2005 21:19:21 -0500

Find a ring with an element that has 2 left inverses.

When I went to the errata of the author, I had found that the hint for using
End(F_2 [x]) was changed.

Now consider the ring End_k(V) where V is a vector space over k with basis
{v_n : n >= 1}. Consider the map

a : V ---> V

that sends v_n to v_(n+1)

Then I have found one left inverse, that is :

b : V ---> V

that sends v_n to v_(n-1) and v_1 to v_1. Note that this is well defined as
a left inverse, but not as a right inverse.

I can't seem to think of anything else though...can anyone think of a
different left inverse of a?

Thanks for any help!

Tony

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